Fundamentals of Thermodynamics

Claus Borgnakke, Richard E. Sonntag

Chapter 6

Entropy - all with Video Answers

Educators

Chapter Questions

Problem 1

When a substance has completed a cycle, $v, u, h,$ and $s$ are unchanged. Did anything happen? Explain.

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Eric Mockensturm

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Problem 2

Assume a heat engine with a given $Q_{H}$. Can you say anything about $Q_{L}$ if the engine is reversible? If it is irreversible?

Uma Kumari

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Problem 3

$C V A$ is the mass inside a piston/cylinder; $C V B$ is that plus part of the wall out to a source of ${ }_{1} Q_{2}$ at $T_{s} .$ Write the entropy equation for the two control volumes, assuming no change of state of the piston mass or walls.

Uma Kumari

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Problem 4

Consider the previous setup with the mass $m_{A}$ and the piston/cylinder of mass $m_{p}$ starting out at two different temperatures (Fig. P6.3). After a while, the temperature becomes uniform without any external heat transfer. Write the entropy equation storage term $\left(S_{2}-S_{1}\right)$ for the total mass.

Uma Kumari

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Problem 5

Water at $100^{\circ} \mathrm{C}$, quality $50 \%$ in a rigid box is heated to $110^{\circ} \mathrm{C} .$ How do the properties $(P, v, x, u,$ and $s)$ change (increase, stay about the same, or decrease)?

Uma Kumari

Numerade Educator

Problem 6

Liquid water at $20^{\circ} \mathrm{C}, 100 \mathrm{kPa}$ is compressed in a piston/cylinder without any heat transfer to a pressure of $200 \mathrm{kPa}$. How do the properties $(T, v, u,$ and $s)$ change (increase, stay about the same, or decrease)?

Uma Kumari

Numerade Educator

Problem 7

A reversible process in a piston/cylinder is shown in Fig. $\mathrm{P} 6.7 .$ Indicate the storage change $u_{2}-u_{1}$ and transfers $_{1} w_{2}$ and $_{1} q_{2}$ as positive, zero, or negative.

Uma Kumari

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Problem 8

A reversible process in a piston/cylinder is shown in Fig. $\mathrm{P} 6.8 .$ Indicate the storage change $u_{2}-u_{1}$ and transfers $_{1} w_{2}$ and $_{1} q_{2}$ as positive, zero, or negative.

Uma Kumari

Numerade Educator

Problem 9

Air at $290 \mathrm{~K}, 100 \mathrm{kPa}$ in a rigid box is heated to $325 \mathrm{~K}$. How do the properties $(P, v, u,$ and $s)$ change (increase, stay about the same, or decrease)?

Uma Kumari

Numerade Educator

Problem 10

Air at $20^{\circ} \mathrm{C}, 100 \mathrm{kPa}$ is compressed in a piston/ cylinder without any heat transfer to a pressure of $200 \mathrm{kPa}$. How do the properties $(T, v, u,$ and $s)$ change (increase, stay about the same, or decrease)?

Uma Kumari

Numerade Educator

Problem 11

Carbon dioxide is compressed to a smaller volume in a polytropic process with $n=1.4$. How do the properties $(u, h, s, P, T)$ change (up, down, or constant)?

Uma Kumari

Numerade Educator

Problem 12

Process $A$ : Air at $300 \mathrm{~K}, 100 \mathrm{kPa}$ is heated to $310 \mathrm{~K}$ at constant pressure. Process $B$ : Air at $1300 \mathrm{~K}$ is heated to $1310 \mathrm{~K}$ at constant $100 \mathrm{kPa}$. Use the table below to compare the property changes.
$$
\begin{array}{l}
\text { Property } \quad \Delta_{A}>\Delta_{B} \quad \Delta_{A} \approx \Delta_{B} \quad \Delta_{A}<\Delta_{B} \\
\hline \Delta=v_{2}-v_{1} \\
\Delta=h_{2}-h_{1} \\
\Delta=s_{2}-s_{1}
\end{array}
$$

Uma Kumari

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Problem 13

Why do we write $\Delta S$ or $S_{2}-S_{1}$, whereas we write $\int d Q / T$ and $_{1} S_{2 \mathrm{gen}} ?$

Uma Kumari

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Problem 14

A reversible heat pump has a flux of $s$ entering as $\dot{Q}_{L} / T_{L} .$ What can you say about the exit flux of $s$ at $T_{H} ?$

Uma Kumari

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Problem 15

An electric baseboard heater receives $1500 \mathrm{~W}$ of electrical power that heats room air, which loses the same amount through the walls and windows. Specify exactly where entropy is generated in that process.

Uma Kumari

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Problem 16

A $500 \mathrm{~W}$ electric space heater with a small fan inside heats air by blowing it over a hot electrical wire. For each control volume, (a) wire at $T_{\text {wire }}$ only, (b) all the room air at $T_{\text {room }},$ and (c) total room plus the heater, specify the storage, entropy transfer terms, and entropy generation as rates (neglect any $\dot{Q}$ through the room walls or windows)

Uma Kumari

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Problem 17

Consider the steam power plant in Example 4.7 and assume an average $T$ in the line between 1 and
2. Show that this cycle satisfies the inequality of Clausius.

Eric Mockensturm

Eric Mockensturm

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Problem 18

A heat engine receives $6 \mathrm{~kW}$ from a $250^{\circ} \mathrm{C}$ source and rejects heat at $30^{\circ} \mathrm{C}$. Examine each of three cases with respect to the inequality of Clausius.
a. $\dot{W}=6 \mathrm{~kW}$
b. $\dot{W}=0 \mathrm{~kW}$
c. Carnot cycle

Eric Mockensturm

Eric Mockensturm

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Problem 19

Use the inequality of Clausius to show that heat transfer from a warm space toward a colder space without work is a possible process, i.e., a heat engine with no work output.

Uma Kumari

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Problem 20

Use the inequality of Clausius to show that heat transfer from a cold space toward a warmer space without work is an impossible process, i.e., a heat pump with no work input.

Uma Kumari

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Problem 21

Assume that the heat engine in Problem 5.34 has a high temperature of $1000 \mathrm{~K}$ and a low temperature of $400 \mathrm{~K}$. What does the inequality of Clausius say about each of the four cases?

Uma Kumari

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Problem 22

Let the steam power plant in Problem 5.30 have a temperature of $700^{\circ} \mathrm{C}$ in the boiler and $40^{\circ} \mathrm{C}$ during the heat rejection in the condenser. Does that satisfy the inequality of Clausius? Repeat the question for the cycle operated in reverse as a refrigerator.

Uma Kumari

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Problem 23

Examine the heat engine in Problem 5.74 to see if it satisfies the inequality of Clausius.

Uma Kumari

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Problem 24

Determine the entropy for these states.
a. Nitrogen, $P=2000 \mathrm{kPa}, 120 \mathrm{~K}$
b. Nitrogen, $120 \mathrm{~K}, v=0.0050 \mathrm{~m}^{3} / \mathrm{kg}$
c. $\mathrm{R}-410 \mathrm{a}, T=25^{\circ} \mathrm{C}, v=0.01 \mathrm{~m}^{3} / \mathrm{kg}$

Uma Kumari

Numerade Educator

Problem 25

Determine the missing property among $P, T, s,$ and $x$ for $\mathrm{R}-410 \mathrm{a}$ at
a. $T=-20^{\circ} \mathrm{C}, v=0.1377 \mathrm{~m}^{3} / \mathrm{kg}$
b. $T=20^{\circ} \mathrm{C}, v=0.01377 \mathrm{~m}^{3} / \mathrm{kg}$
c. $P=200 \mathrm{kPa}, s=1.409 \mathrm{~kJ} / \mathrm{kgK}$

Uma Kumari

Numerade Educator

Problem 26

Find the missing properties of $P, v, s,$ and $x$ for ammonia $\left(\mathrm{NH}_{3}\right)$ at
a. $T=65^{\circ} \mathrm{C}, P=600 \mathrm{kPa}$
b. $T=20^{\circ} \mathrm{C}, u=800 \mathrm{~kJ} / \mathrm{kg}$
c. $T=50^{\circ} \mathrm{C}, v=0.1185 \mathrm{~m}^{3} / \mathrm{kg}$

Uma Kumari

Numerade Educator

Problem 27

Find the entropy for the following water states and indicate each state on a $T-s$ diagram relative to the two-phase region.
a. $250^{\circ} \mathrm{C}, v=0.02 \mathrm{~m}^{3} / \mathrm{kg}$
b. $250^{\circ} \mathrm{C}, 2000 \mathrm{kPa}$
c. $-2{ }^{\circ} \mathrm{C}, 100 \mathrm{kPa}$

Uma Kumari

Numerade Educator

Problem 28

Find the missing properties of $P, v, s,$ and $x$ for $\mathrm{CO}_{2}$ and indicate each state on a $T-s$ diagram relative to the two-phase region.
a. $-20^{\circ} \mathrm{C}, 2000 \mathrm{kPa}$
b. $20^{\circ} \mathrm{C}, s=1.49 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$
c. $-10^{\circ} \mathrm{C}, s=1 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$

Uma Kumari

Numerade Educator

Problem 29

Determine the missing properties among $(T, P, v, s)$
a. $\mathrm{H}_{2} \mathrm{O} \quad 20^{\circ} \mathrm{C}, v=0.001000 \mathrm{~m}^{3} / \mathrm{kg}$
$\begin{array}{ll}\text { b. R-410a } & 400 \mathrm{kPa}, s=1.17 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\end{array}$
$\begin{array}{ll}\text { c. } \mathrm{NH}_{3} & 10^{\circ} \mathrm{C}, v=0.1 \mathrm{~m}^{3} / \mathrm{kg}\end{array}$
$\begin{array}{ll}\text { d. } \mathrm{N}_{2} & 101.3 \mathrm{kPa}, s=3.5 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\end{array}$

Uma Kumari

Numerade Educator

Problem 30

Two kilograms of water at $120^{\circ} \mathrm{C}$ with a quality of $25 \%$ has its temperature raised $20^{\circ} \mathrm{C}$ in a constantvolume process. What are the new quality and specific entropy? Two kilograms of water at $400 \mathrm{kPa}$ with a quality of $25 \%$ has its temperature raised $20^{\circ} \mathrm{C}$ in a constantpressure process. What is the change in entropy?

Uma Kumari

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Problem 31

Two kilograms of water at $400 \mathrm{kPa}$ with a quality of $25 \%$ has its temperature raised $20^{\circ} \mathrm{C}$ in a constantpressure process. What is the change in entropy?

Uma Kumari

Numerade Educator

Problem 32

Saturated liquid water at $20^{\circ} \mathrm{C}$ is compressed to a higher pressure with constant temperature. Find the changes in $u$ and $s$ when the final pressure is
a. $500 \mathrm{kPa}$
b. $2000 \mathrm{kPa}$
c. $20000 \mathrm{kPa}$

Eric Mockensturm

Eric Mockensturm

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Problem 33

Saturated vapor water at $250^{\circ} \mathrm{C}$ is expanded to a lower pressure with constant temperature. Find the changes in $u$ and $s$ when the final pressure is
a. $100 \mathrm{kPa}$
b. $50 \mathrm{kPa}$
c. $10 \mathrm{kPa}$

Uma Kumari

Numerade Educator

Problem 34

Determine the missing property among $P, T, s, x$ for the following states:
a. Ammonia $25^{\circ} \mathrm{C}, v=0.10 \mathrm{~m}^{3} / \mathrm{kg}$
b. Ammonia $\quad 1000 \mathrm{kPa}, s=5.2 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$
c. R-410a $\quad 500 \mathrm{kPa}, s=1.4 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$
d. R-410a $\quad 50^{\circ} \mathrm{C}, s=0.8 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$

Uma Kumari

Numerade Educator

Problem 35

In a Carnot engine with ammonia as the working fluid, the high temperature is $60^{\circ} \mathrm{C}$ and as $Q_{H}$ is received, the ammonia changes from saturated liquid to saturated vapor. The ammonia pressure at the low temperature is $190 \mathrm{kPa}$. Find $T_{L},$ the cycle thermal efficiency, the heat added per kilogram, and the entropy, $s$, at the beginning of the heat rejection process.

Uma Kumari

Numerade Educator

Problem 36

Consider a Carnot-cycle heat pump with $\mathrm{R}-410 \mathrm{a}$ as the working fluid. Heat is rejected from the $\mathrm{R}-410 \mathrm{a}$ at $35^{\circ} \mathrm{C}$, during which process the $\mathrm{R}-410$ a changes from saturated vapor to saturated liquid. The heat is transferred to the $\mathrm{R}-410 \mathrm{a}$ at $0^{\circ} \mathrm{C}$.
a. Show the cycle on a $T-s$ diagram.
b. Find the quality of the $\mathrm{R}-410 \mathrm{a}$ at the beginning and end of the isothermal heat addition process at $0^{\circ} \mathrm{C}$.
c. Determine the COP for the cycle.

Uma Kumari

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Problem 37

Do Problem 6.36 using refrigerant $\mathrm{R}-134 \mathrm{a}$ instead of $R-410 a$.

Uma Kumari

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Problem 38

Water is used as the working fluid in a Carnot-cycle heat engine, where it changes from saturated liquid to saturated vapor at $200^{\circ} \mathrm{C}$ as heat is added. Heat is rejected in a constant-pressure process (also constant $T$ ) at $20 \mathrm{kPa}$. The heat engine powers a Carnotcycle refrigerator that operates between $-15^{\circ} \mathrm{C}$ and $+20^{\circ} \mathrm{C}$, shown in Fig. $\mathrm{P} 6.38 .$ Find the heat added to the water per kilogram of water. How much heat should be added to the water in the heat engine so that the refrigerator can remove $1 \mathrm{~kJ}$ from the cold space?

Uma Kumari

Numerade Educator

Problem 39

Water at $1 \mathrm{MPa}, 250^{\circ} \mathrm{C}$ is expanded in a piston/ cylinder to $200 \mathrm{kPa}, x=1.0$ in a reversible process. Find the sign for the work and the sign for the heat transfer.

Uma Kumari

Numerade Educator

Problem 40

$\mathrm{R}-410 \mathrm{a}$ at $1 \mathrm{MPa}$ and $60^{\circ} \mathrm{C}$ is expanded in a piston cylinder to $500 \mathrm{kPa}, 40^{\circ} \mathrm{C}$ in a reversible process. Find the sign for both the work and the heat transfer for this process.

Uma Kumari

Numerade Educator

Problem 41

A piston/cylinder compressor takes $\mathrm{R}-410 \mathrm{a}$ as saturated vapor $500 \mathrm{kPa}$ and compresses it in a reversible adiabatic process to $3000 \mathrm{kPa}$. Find the final temperature and the specific compression work.

Uma Kumari

Numerade Educator

Problem 42

A piston/cylinder receives $\mathrm{R}-410 \mathrm{a}$ at $500 \mathrm{kPa}$ and compresses it in a reversible adiabatic process to $1800 \mathrm{kPa}, 60^{\circ} \mathrm{C}$. Find the initial temperature.

Uma Kumari

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Problem 43

Compression and heat transfer bring carbon dioxide in a piston/cylinder from $1400 \mathrm{kPa}, 20^{\circ} \mathrm{C}$ to saturated vapor in an isothermal process. Find the specific heat transfer and the specific work.

Uma Kumari

Numerade Educator

Problem 44

A piston/cylinder maintaining constant pressure contains $0.1 \mathrm{~kg}$ saturated liquid water at $100^{\circ} \mathrm{C}$. It is now boiled to become saturated vapor in a reversible process. Find the work term and then the heat transfer from the energy equation. Find the heat transfer from the entropy equation; is it the same?

Uma Kumari

Numerade Educator

Problem 45

A piston/cylinder contains $0.25 \mathrm{~kg}$ of $\mathrm{R}-134 \mathrm{a}$ at $100 \mathrm{kPa}$. It will be compressed in an adiabatic reversible process to $400 \mathrm{kPa}$ and should be at $70^{\circ} \mathrm{C}$. What should the initial temperature be?

Uma Kumari

Numerade Educator

Problem 46

A piston/cylinder contains $0.5 \mathrm{~kg}$ of water at $200 \mathrm{kPa}, 300^{\circ} \mathrm{C},$ and it now cools to $150^{\circ} \mathrm{C}$ in an
isobaric process. The heat goes into a heat engine that rejects heat to the ambient at $25^{\circ} \mathrm{C}$ (shown in Fig. $\mathrm{P} 6.46$ ), and the whole process is assumed to be reversible. Find the heat transfer out of the water and the work given out by the heat engine.

Nicholas Mogoi

Numerade Educator

Problem 47

A cylinder fitted with a piston contains ammonia at $50^{\circ} \mathrm{C}, 20 \%$ quality with a volume of $1 \mathrm{~L}$. The ammonia expands slowly, and during this process heat is transferred to maintain a constant temperature. The process continues until all the liquid is gone. Determine the work and heat transfer for this
process.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 48

Water in a piston/cylinder at $400^{\circ} \mathrm{C}, 2000 \mathrm{kPa}$ is expanded in a reversible adiabatic process. The specific work is measured to be $415.72 \mathrm{~kJ} / \mathrm{kg}$ out. Find the final $P$ and $T$ and show the $P-v$ and $T-s$ diagrams for the process.

Uma Kumari

Numerade Educator

Problem 49

A piston/cylinder has $2 \mathrm{~kg}$ water at $1000 \mathrm{kPa}, 200^{\circ} \mathrm{C}$ that is now cooled with a constant loading on the piston. This isobaric process ends when the water reaches a state of saturated liquid. Find the work and heat transfer and sketch the process in both a $P-v$ and a $T-s$ diagram.

Uma Kumari

Numerade Educator

Problem 50

One kilogram of water at $300^{\circ} \mathrm{C}$ expands against a piston in a cylinder until it reaches ambient pressure, $100 \mathrm{kPa}$, at which point the water has a quality of $90.2 \% .$ It may be assumed that the expansion is reversible and adiabatic. What was the initial pressure in the cylinder, and how much work is done by the water?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 51

Water at $1000 \mathrm{kPa}, 250^{\circ} \mathrm{C}$ is brought to saturated vapor in a rigid container, shown in Fig. $\mathrm{P} 6.51 .$ Find the final $T$ and the specific heat transfer in this isometric process.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 52

Estimate the specific heat transfer from the area in a $T-s$ diagram and compare it to the correct value for the states and process in Problem $6.51 .$

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 53

A closed tank, $V=10 \mathrm{~L}$, containing $5 \mathrm{~kg}$ of water initially at $25^{\circ} \mathrm{C},$ is heated to $150^{\circ} \mathrm{C}$ by a heat pump that is receiving heat from the surroundings at $25^{\circ} \mathrm{C}$. Assume that this process is reversible. Find the heat transfer to the water and its change in entropy.

Uma Kumari

Numerade Educator

Problem 54

A piston/cylinder has $2 \mathrm{~kg}$ of $\mathrm{R}-410 \mathrm{a}$ at $60^{\circ} \mathrm{C}$ $100 \mathrm{kPa}$ that is compressed to $1000 \mathrm{kPa}$. The process happens so slowly that the temperature is constant. Find the heat transfer and work for the process, assuming it to be reversible.

Uma Kumari

Numerade Educator

Problem 55

A heavily insulated cylinder/piston contains ammonia at $1200 \mathrm{kPa}, 60^{\circ} \mathrm{C}$. The piston is moved, expanding the ammonia in a reversible process until the temperature is $-20^{\circ} \mathrm{C}$. During the process, $200 \mathrm{~kJ}$ of work is given out by the ammonia. What was the initial volume of the cylinder?

Uma Kumari

Numerade Educator

Problem 56

Water at $1000 \mathrm{kPa}, 250^{\circ} \mathrm{C}$ is brought to saturated vapor in a piston/cylinder with an isothermal process. Find the specific work and heat transfer. Estimate the specific work from the area in the $P-v$ diagram and compare it to the correct value.

Uma Kumari

Numerade Educator

Problem 57

A rigid, insulated vessel contains superheated vapor steam at $3 \mathrm{MPa}, 400^{\circ} \mathrm{C}$. A valve on the vessel is opened, allowing steam to escape, as shown in Fig. $\mathrm{P} 6.57 .$ The overall process is irreversible, but the steam remaining inside the vessel goes through a reversible adiabatic expansion. Determine the fraction of steam that has escaped when the final state inside is saturated vapor.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 58

Water at $100 \mathrm{kPa}, 25^{\circ} \mathrm{C}$ is brought to the boiling point in a piston/cylinder with an isobaric process. The heat is supplied by a heat pump with the cold side at the ambient temperature of $25^{\circ} \mathrm{C}$. Assume that the whole process is reversible and find the work input to the heat pump per $\mathrm{kg}$ of water.

Uma Kumari

Numerade Educator

Problem 59

Water at $1000 \mathrm{kPa}, 200^{\circ} \mathrm{C}$ is brought to saturated vapor in a piston/cylinder with an isobaric process. Find the specific work and heat transfer. Estimate the specific heat transfer from the area in a $T-s$ diagram and compare it to the correct value.

Uma Kumari

Numerade Educator

Problem 60

Two $5-\mathrm{kg}$ blocks of steel, one at $250^{\circ} \mathrm{C}$ and the other at $25^{\circ} \mathrm{C}$, come in thermal contact. Find the final temperature and the change in entropy of the steel.

Uma Kumari

Numerade Educator

Problem 61

A rigid tank of $1.2-\mathrm{kg}$ steel contains $1.5 \mathrm{~kg}$ of $\mathrm{R}-134 \mathrm{a}$ at $40^{\circ} \mathrm{C}, 500 \mathrm{kPa}$. The tank is placed in a
refrigerator that brings it to $-20^{\circ} \mathrm{C}$. Find the process heat transfer and the combined steel and R-134a change in entropy.

Uma Kumari

Numerade Educator

Problem 62

A large slab of concrete, $5 \times 8 \times 0.3 \mathrm{~m},$ is used as a thermal storage mass in a solar-heated house. If the slab cools overnight from $23^{\circ} \mathrm{C}$ to $18^{\circ} \mathrm{C}$ in an $18^{\circ} \mathrm{C}$ house, what is the net entropy change associated with this process?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 63

A foundry form box with $25 \mathrm{~kg}$ of $200^{\circ} \mathrm{C}$ hot sand is dumped into a bucket with $50 \mathrm{~L}$ water at $15^{\circ} \mathrm{C}$. Assuming no heat transfer with the surroundings and no boiling away of liquid water, calculate the net entropy change for the mass.

Uma Kumari

Numerade Educator

Problem 64

Heat transfer to a block of 1.5 -kg ice at $-10^{\circ} \mathrm{C}$ melts it to liquid at $10^{\circ} \mathrm{C}$ in a kitchen. Find the entropy change of the water.

Uma Kumari

Numerade Educator

Problem 65

In a sink, $5 \mathrm{~L}$ of water at $70^{\circ} \mathrm{C}$ is combined with $1 \mathrm{~kg}$ of aluminum pots, $1 \mathrm{~kg}$ of flatware (steel), and $1 \mathrm{~kg}$ of glass, all put in at $20^{\circ} \mathrm{C}$. What is the final uniform temperature and change in stored entropy, neglecting any heat loss and work?

Uma Kumari

Numerade Educator

Problem 66

A piston/cylinder has constant pressure of $2000 \mathrm{kPa}$ with water at $20^{\circ} \mathrm{C}$. It is now heated to $100^{\circ} \mathrm{C}$. Find
the heat transfer and the entropy change using the steam tables. Repeat the calculation using constant heat capacity and incompressibility.

Uma Kumari

Numerade Educator

Problem 67

A 4 - $\mathrm{L}$ jug of milk at $25^{\circ} \mathrm{C}$ is placed in your refrigerator, where it is cooled down to the refrigerator's inside constant temperature of $5^{\circ} \mathrm{C}$. Assume the milk has the property of liquid water and find the entropy change of the milk.

Uma Kumari

Numerade Educator

Problem 68

A constant pressure container of $1.2 \mathrm{~kg}$ steel contains $1.5 \mathrm{~kg}$ of $\mathrm{R}-134 \mathrm{a}$ at $40 \mathrm{C}, 500 \mathrm{kPa}$. The container is placed in a refrigerator that brings it to $-20^{\circ} \mathrm{C}$. Find the process heat transfer and the combined steel and $\mathrm{R}-134 \mathrm{a}$ change in entropy.

Uma Kumari

Numerade Educator

Problem 69

A $10-\mathrm{kg}$ steel container is cured at $500^{\circ} \mathrm{C}$. Liquid water at $15^{\circ} \mathrm{C}, 100 \mathrm{kPa}$ is added to the container, so the final uniform temperature of the steel and the water becomes $50^{\circ} \mathrm{C}$. Neglect any water that might evaporate during the process and any air in the container. How much water should be added, and how much was the entropy changed?

Uma Kumari

Numerade Educator

Problem 70

A pan in an auto shop contains $5 \mathrm{~L}$ of engine oil at $20^{\circ} \mathrm{C}, 100 \mathrm{kPa} .$ Now $3 \mathrm{~L}$ of oil at $100^{\circ} \mathrm{C}$ is mixed
into the pan. Neglect any work term and find the final temperature and the entropy change.

Uma Kumari

Numerade Educator

Problem 71

A computer CPU chip consists of $50 \mathrm{~g}$ silicon, $20 \mathrm{~g}$ copper, and 50 g polyvinyl chloride (plastic). It heats from $15^{\circ} \mathrm{C}$ to $75^{\circ} \mathrm{C}$ as the computer is turned on. How much did the entropy increase?

Uma Kumari

Numerade Educator

Problem 72

A $5-\mathrm{kg}$ aluminum radiator holds $2 \mathrm{~kg}$ of liquid $\mathrm{R}-134 \mathrm{a}$ at $-10^{\circ} \mathrm{C}$. The setup is brought indoors and heated with $220 \mathrm{~kJ}$. Find the final temperature and the change in entropy of the mass.

Uma Kumari

Numerade Educator

Problem 73

A $12-\mathrm{kg}$ steel container has $0.2 \mathrm{~kg}$ superheated water vapor at $1000 \mathrm{kPa}$, both at $200^{\circ} \mathrm{C}$. The total mass is now cooled to the ambient temperature, $30^{\circ} \mathrm{C}$. How much heat transfer was taken out and what is the steel-water entropy change?

Uma Kumari

Numerade Educator

Problem 74

Find the total work the heat engine can give out as it receives energy from the rock bed as, described in Problem 5.60 (see Fig. $\mathrm{P} 6.74$ ). Hint: write the entropy balance equation for the control volume that is the combination of the rock bed and the heat engine.

Uma Kumari

Numerade Educator

Problem 75

Consider Problem 6.60 if the two blocks of steel exchange energy through a heat engine similar to the setup in Problem $6.74 .$ Find the work output of the heat engine.

Uma Kumari

Numerade Educator

Problem 76

Two kilograms of liquid lead initially at $400^{\circ} \mathrm{C}$ is poured into a form. It then cools at constant pressure down to room temperature of $20^{\circ} \mathrm{C}$ as heat is transferred to the room. The melting point of lead is $327^{\circ} \mathrm{C}$ and the enthalpy change between the phases, $h_{\mathrm{if}},$ is $24.6 \mathrm{~kJ} / \mathrm{kg} .$ The specific heats are found in Tables $\mathrm{A} .3$ and $\mathrm{A} .4 .$ Calculate the net entropy change for the mass.

Uma Kumari

Numerade Educator

Problem 77

Air inside a rigid tank is heated from 300 to $350 \mathrm{~K}$. Find the entropy increase $s_{2}-s_{1} .$ What is the entropy increase if the tank is heated from 1300 to $1350 \mathrm{~K} ?$

Uma Kumari

Numerade Educator

Problem 78

A rigid tank contains 1 kg methane at $500 \mathrm{~K}, 1500$ $\mathrm{kPa}$. It is now cooled down to $300 \mathrm{~K}$. Find the heat transfer and the change in entropy using ideal gas.

Uma Kumari

Numerade Educator

Problem 79

Three kilograms of air is in a piston/cylinder keeping constant pressure at $27^{\circ} \mathrm{C}, 300 \mathrm{kPa}$. It is now heated to $500 \mathrm{~K}$. Plot the process path in a $T-s$ diagram and find the heat transfer in the process.

Uma Kumari

Numerade Educator

Problem 80

A piston/cylinder setup contains air at $100 \mathrm{kPa}$ $400 \mathrm{~K}$ that is compressed to a final pressure of $1000 \mathrm{kPa} .$ Consider two different processes: (a) a reversible adiabatic process and (b) a reversible isothermal process. Show both processes in $P-v$ and a $T-s$ diagram. Find the final temperature and the specific work for both processes.

Uma Kumari

Numerade Educator

Problem 81

Prove that the two relations for changes in $s$, Eqs. 6.16 and $6.17,$ are equivalent once we assume constant specific heat. Hint: recall the relation for specific heat in Eq. $3.27 .$

Uma Kumari

Numerade Educator

Problem 82

A closed rigid container is filled with $1.5 \mathrm{~kg}$ water at $100 \mathrm{kPa}, 55^{\circ} \mathrm{C}, 1 \mathrm{~kg}$ of stainless steel and $0.5 \mathrm{~kg}$
of polyvinyl chloride, both at $20^{\circ} \mathrm{C}$ and $0.1 \mathrm{~kg}$ of hot air at $400 \mathrm{~K}, 100 \mathrm{kPa}$. It is now left alone, with no external heat transfer and no water vaporizes. Find the final temperature and the change in entropy of the masses.

Uma Kumari

Numerade Educator

Problem 83

Water at $150^{\circ} \mathrm{C}, 400 \mathrm{kPa}$ is brought to $1200^{\circ} \mathrm{C}$ in a constant-pressure process. Find the change in specific entropy using (a) the steam tables, (b) the ideal gas water Table $\mathrm{A} .8$, and (c) the specific heat from Table A.5.

Uma Kumari

Numerade Educator

Problem 84

R-410a at $400 \mathrm{kPa}$ is brought from $20^{\circ} \mathrm{C}$ to $120^{\circ} \mathrm{C}$ in a constant-pressure process. Evaluate the change in specific entropy using Table $\mathrm{B} .4$ and using ideal gas with $C_{p}=0.81 \mathrm{~kJ} / \mathrm{kgK}$.

Uma Kumari

Numerade Educator

Problem 85

$\mathrm{R}-410 \mathrm{a}$ at $300 \mathrm{kPa}, 20^{\circ} \mathrm{C}$ is brought to $200^{\circ} \mathrm{C}$ in
a constant-volume process. Evaluate the change in specific entropy using Table $\mathrm{B} .4$ and using ideal gas with $C_{v}=0.695 \mathrm{~kJ} / \mathrm{kgK}$.

Uma Kumari

Numerade Educator

Problem 86

Consider a small air pistol (Fig. $\mathrm{P} 6.86$ ) with a cylinder volume of $1 \mathrm{~cm}^{3}$ at $250 \mathrm{kPa}, 27^{\circ} \mathrm{C}$. The bullet acts as a piston initially held by a trigger. The bullet is released, so the air expands in an adiabatic process. If the pressure should be $120 \mathrm{kPa}$ as the bullet leaves the cylinder, find the final volume and the work done by the air.

Uma Kumari

Numerade Educator

Problem 87

Oxygen gas in a piston/cylinder at $300 \mathrm{~K}, 100 \mathrm{kPa}$ with a volume of $0.1 \mathrm{~m}^{3}$ is compressed in a reversible adiabatic process to a final temperature of $700 \mathrm{~K}$. Find the final pressure and volume using Table $A .5$ and repeat the process with Table $A .8$.

Uma Kumari

Numerade Educator

Problem 88

Air in a rigid tank is at $100 \mathrm{kPa}, 300 \mathrm{~K}$ with a volume of $0.75 \mathrm{~m}^{3}$. The tank is heated to $400 \mathrm{~K}$, state 2 . Now one side of the tank acts as a piston, letting the air expand slowly at constant temperature to state 3 with a volume of $1.5 \mathrm{~m}^{3}$. Find the entropy at states $1,2,$ and 3

Uma Kumari

Numerade Educator

Problem 89

An insulated piston/cylinder setup contains carbon dioxide gas at $800 \mathrm{kPa}, 300 \mathrm{~K}$ that is then compressed to 6 MPa in a reversible adiabatic process. Calculate the final temperature and the specific work using (a) ideal gas Tables $A .8$ and $(b)$ using constant specific heats in Table A.5.

Uma Kumari

Numerade Educator

Problem 90

Extend the previous problem to solve using Table B.3.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 91

A handheld pump for a bicycle (Fig. $\mathrm{P} 6.91$ ) has a volume of $25 \mathrm{~cm}^{3}$ when fully extended. You now press the plunger (piston) in while holding your thumb over the exit hole so that an air pressure of $300 \mathrm{kPa}$ is obtained. The outside atmosphere is at $P_{0}, T_{0} .$ Consider two cases: (1) it is done quickly $(\sim 1 \mathrm{~s}),$ and (2) it is done very slowly $(\sim 1 \mathrm{~h})$
a. State the assumptions about the process for each case
b. Find the final volume and temperature for both cases.

Uma Kumari

Numerade Educator

Problem 92

A piston/cylinder, shown in Fig. $\mathrm{P} 6.92,$ contains air at $1380 \mathrm{~K}, 15 \mathrm{MPa},$ with $V_{1}=10 \mathrm{~cm}^{3}, A_{\mathrm{cyl}}=5 \mathrm{~cm}^{2}$
The piston is released, and just before the piston exits the end of the cylinder, the pressure inside is $200 \mathrm{kPa}$. If the cylinder is insulated, what is its length? How much work is done by the air inside?

Uma Kumari

Numerade Educator

Problem 93

Argon in a light bulb is at $90 \mathrm{kPa}, 20^{\circ} \mathrm{C}$ when it is turned on and electricity input now heats it to $60^{\circ} \mathrm{C}$. Find the entropy increase of the argon gas.

Uma Kumari

Numerade Educator

Problem 94

We wish to obtain a supply of cold helium gas by applying the following technique. Helium contained in a cylinder under ambient conditions, $100 \mathrm{kPa}$ $20^{\circ} \mathrm{C}$, is compressed in a reversible isothermal process to $600 \mathrm{kPa}$, after which the gas is expanded back to $100 \mathrm{kPa}$ in a reversible adiabatic process.
a. Show the process on a $T-s$ diagram.
b. Calculate the final temperature and the net work per kilogram of helium.

Uma Kumari

Numerade Educator

Problem 95

A $1-\mathrm{m}^{3}$ insulated, rigid tank contains air at $800 \mathrm{kPa}$, $25^{\circ} \mathrm{C}$. A valve on the tank is opened, and the pressure inside quickly drops to $150 \mathrm{kPa}$, at which point the valve is closed. Assuming that the air remaining inside has undergone reversible adiabatic expansion, calculate the mass withdrawn during the process.

Uma Kumari

Numerade Educator

Problem 96

Two rigid, insulated tanks are connected with a pipe and valve. One tank has $0.5 \mathrm{~kg}$ air at $200 \mathrm{kPa}, 300 \mathrm{~K}$ and the other has $0.75 \mathrm{~kg}$ air at $100 \mathrm{kPa}, 400 \mathrm{~K}$. The valve is opened, and the air comes to a single uniform state without any heat transfer. Find the final temperature and the change in entropy of the air.

Uma Kumari

Numerade Educator

Problem 97

Two rigid tanks, shown in Fig. $\mathrm{P} 6.97,$ each contains $10 \mathrm{~kg} \mathrm{~N}_{2}$ gas at $1000 \mathrm{~K}, 500 \mathrm{kPa}$. They are now thermally connected to a reversible heat pump, which heats one tank and cools the other, with no heat transfer to the surroundings. When one tank is heated to $1500 \mathrm{~K}$, the process stops. Find the final $(P, T)$ in both tanks and the work input to the heat pump, assuming constant heat capacities.

Uma Kumari

Numerade Educator

Problem 98

A hydrogen gas in a piston/cylinder assembly at $300 \mathrm{~K}, 100 \mathrm{kPa}$ with a volume of $0.1 \mathrm{~m}^{3}$ is now slowly compressed to a volume of $0.01 \mathrm{~m}^{3}$ while cooling in a reversible isothermal process. What is the final pressure, the heat transfer, and the change in entropy?

Uma Kumari

Numerade Educator

Problem 99

A rigid tank contains $4 \mathrm{~kg}$ air at $300^{\circ} \mathrm{C}, 4$ MPa that acts as the hot energy reservoir for a heat engine with its cold side at $20^{\circ} \mathrm{C}$, shown in Fig. $\mathrm{P} 6.99 .$ Heat transfer to the heat engine cools the air down in a reversible process to a final $20^{\circ} \mathrm{C}$ and then stops. Find the final air pressure and the work output of the heat engine.

Uma Kumari

Numerade Educator

Problem 101

Repeat the previous problem for the gas carbon monoxide.

Uma Kumari

Numerade Educator

Problem 102

A nitrogen gas goes through a polytropic process with $n=1.3$ in a piston/cylinder arrangement. It starts out at $600 \mathrm{~K}, 600 \mathrm{kPa}$ and ends at $800 \mathrm{~K}$. Is the heat transfer positive, negative, or zero?

Uma Kumari

Numerade Educator

Problem 103

A cylinder/piston contains 1 kg methane gas at $100 \mathrm{kPa}, 300 \mathrm{~K}$. The gas is compressed reversibly to a pressure of $800 \mathrm{kPa}$. Calculate the work required if the process is adiabatic.

Uma Kumari

Numerade Educator

Problem 104

Do the previous problem but assume that the process is isothermal.

Uma Kumari

Numerade Educator

Problem 105

A piston/cylinder contains air at $300 \mathrm{~K}, 100 \mathrm{kPa}$. It is now compressed in a reversible adiabatic process to a volume seven times as small. Use constant
heat capacity and find the final pressure and temperature, the specific work, and the specific heat transfer for the process.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 105

A cylinder containing $\mathrm{R}-134 \mathrm{a}$ at $60 \mathrm{~F}, 30 \mathrm{lbf} / \mathrm{in} .{ }^{2}$
has an initial volume of $1 \mathrm{ft}^{3}$. A piston compresses the $\mathrm{R}-134 \mathrm{a}$ in a reversible isothermal process until it reaches the saturated vapor state. Calculate the work and heat transfer required to accomplish this process.

Uma Kumari

Numerade Educator

Problem 106

A piston/cylinder contains pure oxygen at $500 \mathrm{~K}$, $600 \mathrm{kPa}$. The piston is moved to a volume such that the final temperature is $700 \mathrm{~K}$ in a polytropic process with exponent $n=1.25 .$ Use ideal gas approximation and constant heat capacity to find the final pressure, the specific work, and the heat transfer.

Uma Kumari

Numerade Educator

Problem 107

Do Problem 6.103 and assume that the process is polytropic with $n=1.15 .$

Uma Kumari

Numerade Educator

Problem 108

Hot combustion air at $2000 \mathrm{~K}$ expands in a polytropic process to a volume six times as large with $n=1.3 .$ Find the specific boundary work and the specific heat transfer using Table A. 7 .

Uma Kumari

Numerade Educator

Problem 109

Air in a piston/cylinder is at $1800 \mathrm{~K}, 7 \mathrm{MPa}$ and expands in a polytropic process with $n=1.5$ to a volume eight times larger. Find the specific work and specific heat transfer in the process using Table A. 7 and draw the $T-s$ diagram.

Uma Kumari

Numerade Educator

Problem 110

Helium in a piston/cylinder at $20^{\circ} \mathrm{C}, 100 \mathrm{kPa}$ is brought to $400 \mathrm{~K}$ in a reversible polytropic process with exponent $n=1.25 .$ You may assume that helium is an ideal gas with constant specific heat. Find the final pressure and both the specific heat transfer and the specific work.

Uma Kumari

Numerade Educator

Problem 111

The power stroke in an internal combustion engine can be approximated with a polytropic expansion. Consider air in a cylinder volume of $0.2 \mathrm{~L}$ at $7 \mathrm{MPa}$ $1800 \mathrm{~K},$ shown in Fig. $\mathrm{P} 6.111 .$ It now expands in a reversible polytropic process with exponent $n=1.5$ through a volume ratio of $10: 1 .$ Show this process on $P-v$ and $T-s$ diagrams, and calculate the work and heat transfer for the process.

Uma Kumari

Numerade Educator

Problem 112

A cylinder/piston contains saturated vapor $\mathrm{R}-410 \mathrm{a}$ at $10^{\circ} \mathrm{C}$; the volume is $10 \mathrm{~L}$. The $\mathrm{R}-410 \mathrm{a}$ is compressed to $2 \mathrm{MPa}, 60^{\circ} \mathrm{C}$ in a reversible (internally) polytropic process. Find the polytropic exponent $n$ and calculate the work and heat transfer.

Uma Kumari

Numerade Educator

Problem 113

Air goes through a polytropic process with $n=1.3$ in a piston/cylinder setup. It starts at $200 \mathrm{kPa}, 300 \mathrm{~K}$ and ends with a pressure of $2200 \mathrm{kPa}$. Find the expansion ratio $v_{2} / v_{1},$ the specific work, and the specific heat transfer.

Uma Kumari

Numerade Educator

Problem 114

A cylinder/piston contains air under ambient conditions $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$ with a volume of $0.3 \mathrm{~m}^{3}$ The air is compressed to $800 \mathrm{kPa}$ in a reversible polytropic process with exponent $n=1.2,$ after which it is expanded back to $100 \mathrm{kPa}$ in a reversible adiabatic process. Show the two processes in $P-v$ and $T-s$ diagrams, and determine the final temperature and the net work.

Uma Kumari

Numerade Educator

Problem 115

Consider a heat transfer of $100 \mathrm{~kJ}$ from $1500 \mathrm{~K}$ hot gases to a steel container at $750 \mathrm{~K}$ that has a heat transfer of the $100 \mathrm{~kJ}$ out to some air at $375 \mathrm{~K}$. Determine the entropy generation in each of the control volumes indicated in Fig. $\mathrm{P} 6.115 .$

Uma Kumari

Numerade Educator

Problem 116

A rigid tank has 0.1 kg saturated vapor $\mathrm{R}-410 \mathrm{a}$ at $0^{\circ} \mathrm{C}$ that is cooled to $-20^{\circ} \mathrm{C}$ by a $-20^{\circ} \mathrm{C}$ heat sink. Show the process in a $T-s$ diagram; find the change in entropy of the $\mathrm{R}-410 \mathrm{a}$, the heat $\sin \mathrm{k},$ and the total entropy generation.

Uma Kumari

Numerade Educator

Problem 117

One kilogram of water at $500^{\circ} \mathrm{C}$ and $1 \mathrm{~kg}$ saturated water vapor, both at $200 \mathrm{kPa}$, are mixed in a constant-pressure and adiabatic process. Find the final temperature and the entropy generation for the process.

Uma Kumari

Numerade Educator

Problem 118

A car uses an average power of 25 hp for a $1-h$ round trip. With a thermal efficiency of $35 \%,$ how much fuel energy was used? What happened to all the energy? What change in entropy took place if we assume an ambient temperature of $20^{\circ} \mathrm{C} ?$.

Uma Kumari

Numerade Educator

Problem 119

A computer chip dissipates $2 \mathrm{~kJ}$ of electric work over time and rejects that work as heat transfer from its $50^{\circ} \mathrm{C}$ surface to $25^{\circ} \mathrm{C}$ air. How much entropy is generated in the chip? How much entropy, if any, is generated outside the chip?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 120

An insulated cylinder/piston contains $\mathrm{R}-134 \mathrm{a}$ at $1 \mathrm{MPa}, 50^{\circ} \mathrm{C},$ with a volume of $100 \mathrm{~L}$. The $\mathrm{R}-134 \mathrm{a}$ expands, moving the piston until the pressure in the cylinder has dropped to $100 \mathrm{kPa}$. It is claimed that the $\mathrm{R}-134 \mathrm{a}$ does $190 \mathrm{~kJ}$ of work against the piston during the process. Is that possible?

Uma Kumari

Numerade Educator

Problem 121

A rigid tank holds $0.75 \mathrm{~kg}$ ammonia at $70^{\circ} \mathrm{C}$ as saturated vapor. The tank is now cooled to $20^{\circ} \mathrm{C}$ by heat transfer to the ambient at $20^{\circ} \mathrm{C}$. Determine the amount of entropy generation during the process.

Uma Kumari

Numerade Educator

Problem 122

The unrestrained expansion of the reactor water in Problem 3.101 has a final state in the two-phase region. Find the entropy generated in the process.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 123

Heat transfer from a $20^{\circ} \mathrm{C}$ kitchen to a block of $1.5 \mathrm{~kg}$ ice at $-10^{\circ} \mathrm{C}$ melts it to liquid at $10^{\circ} \mathrm{C}$. How much entropy is generated?

Uma Kumari

Numerade Educator

Problem 124

Ammonia is contained in a rigid sealed tank of unknown quality at $0^{\circ} \mathrm{C}$. When heated in boiling water to $100^{\circ} \mathrm{C}$ its, pressure reaches $1200 \mathrm{kPa}$. Find the initial quality, the heat transfer to the ammonia, and the total entropy generation.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 125

Water in a piston/cylinder is at $101 \mathrm{kPa}, 25^{\circ} \mathrm{C}$ and mass $0.5 \mathrm{~kg}$. The piston rests on some stops, and the pressure should be $1000 \mathrm{kPa}$ to float the piston. We now heat the water from a $200^{\circ} \mathrm{C}$ reservoir, so the volume becomes five times the initial value. Find the total heat transfer and the entropy generation.

Uma Kumari

Numerade Educator

Problem 126

Do Problem 6.125 assuming the piston/cylinder is $1.5 \mathrm{~kg}$ of steel and has the same temperature as the water at any time.

Uma Kumari

Numerade Educator

Problem 127

A cylinder fitted with a movable piston contains water at $3 \mathrm{MPa}, 50 \%$ quality, at which point the volume is $20 \mathrm{~L}$. The water now expands to $1.2 \mathrm{MPa}$ as a result of receiving $600 \mathrm{~kJ}$ of heat from a large source at $300^{\circ} \mathrm{C}$. It is claimed that the water does
$124 \mathrm{~kJ}$ of work during this process. Is this possible?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 128

A piston/cylinder device keeping a constant pressure has $1 \mathrm{~kg}$ water at $20^{\circ} \mathrm{C}$ and $1 \mathrm{~kg}$ of water at $100^{\circ} \mathrm{C},$ both at $500 \mathrm{kPa}$ separated by a thin membrane, shown in Fig. $\mathrm{P} 6.128 .$ The membrane is broken and the water comes to a uniform state, with no external heat transfer. Find the final temperature and the entropy generation for the process.

Uma Kumari

Numerade Educator

Problem 129

Reconsider problem 3.109 where carbon dioxide is compressed from $-20^{\circ} \mathrm{C}, x=0.75$ to a state of $3 \mathrm{MPa}, 20^{\circ} \mathrm{C}$ in a piston/cylinder where pressure is linear in volume. Assume heat transfer is from a reservoir at $100^{\circ} \mathrm{C}$ and find the specific entropy generation in the process (external to the carbon dioxide).

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 130

A piston/cylinder contains $1 \mathrm{~kg}$ water at $150 \mathrm{kPa}$ $20^{\circ} \mathrm{C} .$ The piston is loaded, so the pressure is linear in volume. Heat is added from a $600^{\circ} \mathrm{C}$ source until the water is at $1 \mathrm{MPa}, 500^{\circ} \mathrm{C}$. Find the heat transfer and the entropy generation.

Uma Kumari

Numerade Educator

Problem 131

A closed, rigid container is filled with $1.5 \mathrm{~kg}$ water at $100 \mathrm{kPa}, 55^{\circ} \mathrm{C}, 1 \mathrm{~kg}$ of stainless steel and $0.5 \mathrm{~kg}$
of polyvinyl chloride, both at $20^{\circ} \mathrm{C}$ and $0.1 \mathrm{~kg}$ of hot air at $400 \mathrm{~K}, 100 \mathrm{kPa}$. It is now left alone, with no external heat transfer, and no water vaporizes. Find the final temperature and the entropy generation for the process.

Uma Kumari

Numerade Educator

Problem 132

A cylinder/piston contains water at $200 \mathrm{kPa}, 200^{\circ} \mathrm{C}$ with a volume of $20 \mathrm{~L}$. The piston is moved slowly, compressing the water to a pressure of $800 \mathrm{kPa}$. The loading on the piston is such that the product $P V$ is a constant. Assuming that the room temperature is $20^{\circ} \mathrm{C}$, show that this process does not violate the second law.

Uma Kumari

Numerade Educator

Problem 133

A rigid steel tank of mass 2.5 kg contains $0.5 \mathrm{~kg}$ $\mathrm{R}-410 \mathrm{a}$ at $0^{\circ} \mathrm{C}$ with a specific volume of $0.01 \mathrm{~m}^{3} / \mathrm{kg}$. The system heats up to the room temperature, $25^{\circ} \mathrm{C}$. Find the process heat transfer and the entropy generation.

Uma Kumari

Numerade Educator

Problem 134

A piston/cylinder has ammonia at $2000 \mathrm{kPa}, 80^{\circ} \mathrm{C}$ with a volume of $0.1 \mathrm{~m}^{3}$. The piston is loaded with a linear spring and outside ambient is at $20^{\circ} \mathrm{C}$, shown in Fig. $\mathrm{P} 6.134 .$ The ammonia now cools down to $20^{\circ} \mathrm{C},$ at which point it has a quality of $15 \% .$ Find the work, the heat transfer, and the total entropy generation in the process.

Uma Kumari

Numerade Educator

Problem 135

One kilogram of ammonia $\left(\mathrm{NH}_{3}\right)$ is contained in a spring-loaded piston/cylinder, similar to Fig. P6. 134 , as saturated liquid at $-20^{\circ} \mathrm{C}$. Heat is added from a reservoir at $100^{\circ} \mathrm{C}$ until a final condition of $800 \mathrm{kPa}, 70^{\circ} \mathrm{C}$ is reached. Find the work, heat transfer, and entropy generation, assuming the process is internally reversible.

Uma Kumari

Numerade Educator

Problem 136

A $5-\mathrm{kg}$ aluminum radiator holds $2 \mathrm{~kg}$ of liquid $\mathrm{R}-134 \mathrm{a},$ both at $-10^{\circ} \mathrm{C}$. The setup is brought indoors and heated with $220 \mathrm{~kJ}$ from a heat source at $100^{\circ} \mathrm{C}$. Find the total entropy generation for the process, assuming the R-134a remains a liquid.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 137

A piston/cylinder of total $1 \mathrm{~kg}$ steel contains $0.5 \mathrm{~kg}$ ammonia at $1600 \mathrm{kPa}$, both masses at $120^{\circ} \mathrm{C}$. Some stops are placed that so a minimum volume is $0.02 \mathrm{~m}^{3},$ shown in Fig. $\mathrm{P} 6.137 .$ Now the whole system is cooled down to $30^{\circ} \mathrm{C}$ by heat transfer to the ambient at $20^{\circ} \mathrm{C}$, and during the process the steel keeps the same temperature as the ammonia. Find the work, the heat transfer, and the total entropy generation in the process.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 138

A piston/cylinder contains $0.1 \mathrm{~kg}$ water at $500^{\circ} \mathrm{C}$, $1000 \mathrm{kPa}$. The piston has a stop at half of the original volume, similar to Fig. $\mathrm{P} 6.137 .$ The water now cools to room temperature, $25^{\circ} \mathrm{C}$. Find the heat transfer and the entropy generation.

Uma Kumari

Numerade Educator

Problem 139

A hollow steel sphere with a $0.5-\mathrm{m}$ inside diameter and a $2 \mathrm{~mm}$ -thick wall contains water at $2 \mathrm{MPa}$, $250^{\circ} \mathrm{C}$. The system (steel plus water) cools to the ambient temperature, $30^{\circ} \mathrm{C}$. Calculate the net entropy change of the system and surroundings for this process.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 140

A cylinder/piston arrangement contains $10 \mathrm{~g}$ ammonia at $20^{\circ} \mathrm{C}$ with a volume of $1 \mathrm{~L}$. There are some stops, so if the piston is at the stops, the volume is $1.4 \mathrm{~L}$. The ammonia is now heated to $200^{\circ} \mathrm{C}$ by a $240^{\circ} \mathrm{C}$ source. The piston and cylinder are made of $0.5 \mathrm{~kg}$ aluminum, and assume that the mass has the same temperature as the ammonia at any time. Find the total heat transfer and the total entropy generation.

Uma Kumari

Numerade Educator

Problem 141

A cylinder/piston arrangement contains $0.1 \mathrm{~kg}$ R-410a of quality $x=0.2534$ at $-20^{\circ}$ C. Stops are mounted, so $V_{\text {stop }}=3 V_{1}$, similar to Fig. $\mathrm{P} 6.140$. The system is now heated to the final temperature of $20^{\circ} \mathrm{C}$ by a $50^{\circ} \mathrm{C}$ source. Find the total entropy generation.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 142

One kilogram of air at $300 \mathrm{~K}$ is mixed with $2 \mathrm{~kg}$ air at $400 \mathrm{~K}$ in a process at a constant $100 \mathrm{kPa}$ and $Q=0$. Find the final $T$ and the entropy generation in the process.

Uma Kumari

Numerade Educator

Problem 143

Air in a rigid tank is at $900 \mathrm{~K}, 500 \mathrm{kPa},$ and it now cools to the ambient temperature of $300 \mathrm{~K}$ by heat loss to the ambient. Find the entropy generation.

Uma Kumari

Numerade Educator

Problem 144

Two rigid, insulated tanks are connected with a pipe and valve. One tank has $0.5 \mathrm{~kg}$ air at $200 \mathrm{kPa}$, $300 \mathrm{~K}$ and the other has $0.75 \mathrm{~kg}$ air at $100 \mathrm{kPa}$ $400 \mathrm{~K}$. The valve is opened and the air comes to a single uniform state, without external heat transfer. Find the final $T$ and $P$ and the entropy generation.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 145

One kilogram air at $100 \mathrm{kPa}$ is mixed with $2 \mathrm{~kg}$ air at $200 \mathrm{kPa}$, both at $300 \mathrm{~K}$, in a rigid, insulated tank. Find the final state $(P, T)$ and the entropy generation in the process.

Uma Kumari

Numerade Educator

Problem 146

A rigid storage tank of $1.5 \mathrm{~m}^{3}$ contains $1 \mathrm{~kg}$ argon at $30^{\circ} \mathrm{C}$. Heat is then transferred to the argon from a furnace operating at $1300^{\circ} \mathrm{C}$ until the specific entropy of the argon has increased by $0.343 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$. Find the total heat transfer and the entropy generated in the process.

Uma Kumari

Numerade Educator

Problem 147

Argon in a light bulb is at $110 \mathrm{kPa}, 90^{\circ} \mathrm{C}$. The light is turned off, so the argon cools to the ambient temperature of $20^{\circ} \mathrm{C}$. Disregard the glass and any other mass and find the specific entropy generation.

Supratim Pal

Numerade Educator

Problem 148

A rigid tank contains $2 \mathrm{~kg}$ air at $200 \mathrm{kPa}$ and ambient temperature, $20^{\circ} \mathrm{C}$. An electric current now passes through a resistor inside the tank. After a total of $100 \mathrm{~kJ}$ of electrical work has crossed the boundary, the air temperature inside is $80^{\circ} \mathrm{C}$. Is this possible?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 149

A piston/cylinder system contains $50 \mathrm{~L}$ air at $300^{\circ} \mathrm{C}, 100 \mathrm{kPa}$, with the piston initially on a set of stops. A total external constant force acts on the piston, so a balancing pressure inside should be $200 \mathrm{kPa}$. The cylinder is made of $2 \mathrm{~kg}$ steel initially at $1300^{\circ} \mathrm{C}$. The system is insulated, so heat transfer occurs only between the steel cylinder and the air. The system comes to equilibrium. Find the final temperature and the entropy generation.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 150

A spring-loaded piston/cylinder contains $1.5 \mathrm{~kg}$ air at $27^{\circ} \mathrm{C}, 160 \mathrm{kPa}$. It is now heated in a process in which pressure is linear in volume, $P=A+B V,$ to twice its initial volume, where it reaches $900 \mathrm{~K}$. Find the work, the heat transfer, and the total entropy generation, assuming a source at $900 \mathrm{~K}$.

Uma Kumari

Numerade Educator

Problem 151

A rigid container with volume $200 \mathrm{~L}$ is divided into two equal volumes by a partition, shown in Fig. P6.151. Both sides contain nitrogen; one side is at $2 \mathrm{MPa}, 200^{\circ} \mathrm{C}$ and the other at $200 \mathrm{kPa}, 100^{\circ} \mathrm{C}$. The partition ruptures, and the nitrogen comes to a uniform state at $70^{\circ} \mathrm{C}$. Assume the temperature of the surroundings is $20^{\circ} \mathrm{C}$. Determine the work done and the net entropy change for the process.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 152

A constant pressure piston/cylinder contains $0.5 \mathrm{~kg}$ air at $300 \mathrm{~K}, 400 \mathrm{kPa}$. Assume the piston/cylinder has a total mass of $1 \mathrm{~kg}$ steel and is at the same temperature as the air at any time. The system is now heated to $1600 \mathrm{~K}$ by heat transfer from a $1700 \mathrm{~K}$ source. Find the entropy generation using constant specific heats for air.

Uma Kumari

Numerade Educator

Problem 153

Do Problem 6.152 using Table A.7.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 154

Nitrogen at $200^{\circ} \mathrm{C}, 300 \mathrm{kPa}$ is in a piston/cylinder, volume $5 \mathrm{~L}$, with the piston locked with a pin. The forces on the piston require a pressure inside of $200 \mathrm{kPa}$ to balance it without the pin. The pin is removed, and the piston quickly comes to its equilibrium position without any heat transfer. Find the final $P, T,$ and $V$ and the entropy generation due to this partly unrestrained expansion.

Uma Kumari

Numerade Educator

Problem 155

The air in the tank of Problem 6.88 receives heat transfer from a reservoir at $450 \mathrm{~K}$. Find the entropy generation due to the process from 1 to 3 .

Uma Kumari

Numerade Educator

Problem 156

One kilogram carbon dioxide at $100 \mathrm{kPa}, 400 \mathrm{~K}$ is mixed with $2 \mathrm{~kg}$ carbon dioxide at $200 \mathrm{kPa}, 2000 \mathrm{~K}$ in a rigid, insulated tank. Find the final state $(P, T)$ and the entropy generation in the process using constant heat capacity from Table A.5.

Uma Kumari

Numerade Educator

Problem 157

Solve Problem 6.156 using Table $A .8$

Uma Kumari

Numerade Educator

Problem 158

Nitrogen at $600 \mathrm{kPa}, 127^{\circ} \mathrm{C}$ is in a $0.5-\mathrm{m}^{3}$ insulated tank connected to a pipe with a valve to a second insulated initially empty tank of volume $0.25 \mathrm{~m}^{3}$, shown in Fig. $\mathrm{P} 6.158 .$ The valve is opened, and the nitrogen fills both tanks at a uniform state. Find the final pressure and temperature and the entropy generation this process causes. Why is the process irreversible?

Uma Kumari

Numerade Educator

Problem 159

A cylinder/piston contains carbon dioxide at $1 \mathrm{MPa}$ $300^{\circ} \mathrm{C}$ with a volume of $200 \mathrm{~L}$. The total external force acting on the piston is proportional to $V^{3}$. This system is allowed to cool to room temperature, $20^{\circ} \mathrm{C}$. What is the total entropy generation for the process?

Uma Kumari

Numerade Educator

Problem 160

The air in the engine cylinder of Problem 3.156 loses the heat to the engine coolant at $100^{\circ} \mathrm{C}$. Find the entropy generation (external to the air) using constant specific heat.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 161

A cylinder/piston contains $100 \mathrm{~L}$ air at $110 \mathrm{kPa}$ $25^{\circ} \mathrm{C}$. The air is compressed in a reversible polytropic process to a final state of $800 \mathrm{kPa}, 500 \mathrm{~K}$. Assume the heat transfer is with the ambient at $25^{\circ} \mathrm{C}$ and determine the polytropic exponent $n$ and the final volume of the air. Find the work done by the air, the heat transfer, and the total entropy generation for the process.

Uma Kumari

Numerade Educator

Problem 162

A room at $22^{\circ} \mathrm{C}$ is heated electrically with $1500 \mathrm{~W}$ to keep a steady temperature. The outside ambient is at $5^{\circ} \mathrm{C}$. Find the flux of $S(=\dot{Q} / T)$ into the room air, into the ambient, and the rate of entropy generation.

Uma Kumari

Numerade Educator

Problem 163

A mass of $3 \mathrm{~kg}$ nitrogen gas at $2000 \mathrm{~K}, V=C$, cools with $500 \mathrm{~W}$. What is $d S / d t ?$

Uma Kumari

Numerade Educator

Problem 164

A heat pump (see Problem 5.49) should upgrade $5 \mathrm{MW}$ of heat at $85^{\circ} \mathrm{C}$ to heat delivered at $150^{\circ} \mathrm{C} .$ For a reversible heat pump, what are the fluxes of entropy into and out of the heat pump?

Uma Kumari

Numerade Educator

Problem 165

Reconsider the heat pump in the previous problem and assume it has a COP of $2.5 .$ What are the fluxes of entropy into and out of the heat pump and the rate of entropy generation inside it?

Uma Kumari

Numerade Educator

Problem 166

A radiant heating lamp powered by electricity has a surface temperature of $1000 \mathrm{~K}$ emitting $500 \mathrm{~W}$. The radiation is absorbed by surfaces at the ambient temperature of $18^{\circ} \mathrm{C}$. Find the total entropy generation and specify where it is made, including how much.

Uma Kumari

Numerade Educator

Problem 167

A heat pump with $\mathrm{COP}=4$ uses $1 \mathrm{~kW}$ of power input to heat a $25^{\circ} \mathrm{C}$ room, drawing energy from the outside at $15^{\circ} \mathrm{C}$. Assume the high/low temperatures in the heat pump are $45^{\circ} \mathrm{C} / 0^{\circ} \mathrm{C}$. Find the total rates of entropy into and out of the heat pump, the rate from the outside at $15^{\circ} \mathrm{C},$ and the rate to the room at $25^{\circ} \mathrm{C}$.

Uma Kumari

Numerade Educator

Problem 168

A window receives $500 \mathrm{~W}$ of heat transfer at the in-side surface of $20^{\circ} \mathrm{C}$ and transmits the $500 \mathrm{~W}$ from its outside surface at $2^{\circ} \mathrm{C}$, continuing to ambient air at $-5^{\circ} \mathrm{C}$. Find the flux of entropy at all three surfaces and the window's rate of entropy generation.

Uma Kumari

Numerade Educator

Problem 169

An amount of power, say $1000 \mathrm{~kW}$, comes from a furnace at $800^{\circ} \mathrm{C}$, going into water vapor at $400^{\circ} \mathrm{C}$. From the water, the power goes to a solid metal at $200^{\circ} \mathrm{C}$ and then into some air at $70^{\circ} \mathrm{C}$. For each location, calculate the flux of $s$ through a surface as $(\dot{Q} / T) .$ What makes the flux larger and larger?

Uma Kumari

Numerade Educator

Problem 170

Room air at $23^{\circ} \mathrm{C}$ is heated by a $2000-\mathrm{W}$ space heater with a surface filament temperature of $700 \mathrm{~K}$, shown in Fig. $\mathrm{P} 6.170 .$ The room at steady state loses the power to the outside which is at $7^{\circ} \mathrm{C}$. Find the rate(s) of entropy generation and specify where it is made.

Uma Kumari

Numerade Educator

Problem 171

A car engine block receives $2 \mathrm{~kW}$ at its surface of $450 \mathrm{~K}$ from hot combustion gases at $1500 \mathrm{~K}$. Near the cooling channel, the engine block transmits $2 \mathrm{~kW}$ out at its $400 \mathrm{~K}$ surface to the coolant flowing at $370 \mathrm{~K}$. Finally, in the radiator, the coolant at $350 \mathrm{~K}$ delivers the $2 \mathrm{~kW}$ to air that is at $25^{\circ} \mathrm{C} .$ Find the rate of entropy generation inside the engine block, inside the coolant, and in the radiator/air combination.

Uma Kumari

Numerade Educator

Problem 172

A farmer runs a heat pump using $2 \mathrm{~kW}$ of power input. It keeps a chicken hatchery at a constant $30^{\circ} \mathrm{C}$ while the room loses $10 \mathrm{~kW}$ to the colder outside ambient air at $10^{\circ} \mathrm{C} .$ Find the COP of the heat pump, the rate of entropy generated in the heat pump and its heat exchangers, and the rate of entropy generated in the heat loss process.

Uma Kumari

Numerade Educator

Problem 173

An insulted cylinder/piston has an initial volume of $0.15 \mathrm{~m}^{3}$ and contains steam at $400 \mathrm{kPa}, 200^{\circ} \mathrm{C}$. The steam is expanded adiabatically, and the work output is measured very carefully to be $30 \mathrm{~kJ}$. It is claimed that the final state of the water is in the
two-phase (liquid and vapor) region. What is your evaluation of the claim?

Uma Kumari

Numerade Educator

Problem 174

A piston/cylinder has a water volume separated in $V_{A}=0.2 \mathrm{~m}^{3}$ and $V_{B}=0.3 \mathrm{~m}^{3}$ by a stiff membrane similar to the one in Fig. $\mathrm{P} 6.128 .$ The initial state in $A$ is $1000 \mathrm{kPa}, x=0.75,$ and in $B$ it is $1600 \mathrm{kPa}$ and $250^{\circ} \mathrm{C}$. Now the membrane ruptures and the water comes to a uniform state at $200^{\circ} \mathrm{C}$ with heat from a $250^{\circ} \mathrm{C}$ source. Find the work, the heat transfer, and the total entropy generation in the process.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 175

The water in the two tanks of Problem 3.214 receives heat transfer from a reservoir at $300^{\circ} \mathrm{C}$. Find the total entropy generation due to this process.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 176

A steel piston/cylinder of 1 kg contains $2.5 \mathrm{~kg}$ ammonia at $50 \mathrm{kPa},-20^{\circ} \mathrm{C}$. Now it is heated to $50^{\circ} \mathrm{C}$ at constant pressure through the bottom of the cylinder from external hot gas at $200^{\circ} \mathrm{C},$ and we assume the steel has the same temperature as the ammonia. Find the heat transfer from the hot gas and the total entropy generation.

Uma Kumari

Numerade Educator

Problem 177

Water in a piston/cylinder, shown in Fig. $\mathrm{P} 6.177,$ is at $1 \mathrm{MPa}, 500^{\circ} \mathrm{C} .$ There are two stops, a lower one at which $V_{\min }=1 \mathrm{~m}^{3}$ and an upper one at $V_{\max }=$ $3 \mathrm{~m}^{3}$. The piston is loaded with a mass and outside atmosphere such that it floats when the pressure is $500 \mathrm{kPa}$. This setup is now cooled to $100^{\circ} \mathrm{C}$ by rejecting heat to the surrounding at $20^{\circ} \mathrm{C} .$ Find the total entropy generated in the process.

Uma Kumari

Numerade Educator

Problem 178

A piston/cylinder contains air at $300 \mathrm{~K}, 100 \mathrm{kPa}$. A reversible polytropic process with $n=1.3$ brings the air to $500 \mathrm{~K}$. Any heat transfer if it comes in is from a $325^{\circ} \mathrm{C}$ reservoir, and if it goes out it is to the ambient at $300 \mathrm{~K}$. Sketch the process in a $P-v$ and a $T-s$ diagram. Find the specific work and specific heat transfer in the process. Find the specific entropy generation (external to the air) in the process.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 179

Assume the heat transfer in Problem 3.213 came from a $200^{\circ} \mathrm{C}$ reservoir. What is the total entropy generation in the process?

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 180

A closed tank, $V=10 \mathrm{~L}$, containing $5 \mathrm{~kg}$ of water initially at $25^{\circ} \mathrm{C}$, is heated to $150^{\circ} \mathrm{C}$ by a heat pump that is receiving heat from the surroundings at $25^{\circ} \mathrm{C}$. Assume that this process is reversible. Find the heat transfer to the water and the work input to the heat pump.

Uma Kumari

Numerade Educator

Problem 181

A resistor in a heating element is a total of $0.5 \mathrm{~kg}$ with specific heat of $0.8 \mathrm{~kJ} / \mathrm{kgK}$. It is now receiving $500 \mathrm{~W}$ of electric power, so it heats from $20^{\circ} \mathrm{C}$ to $180^{\circ} \mathrm{C}$. Neglect external heat loss and find the time the process took and the entropy generation.

Uma Kumari

Numerade Educator

Problem 182

Two tanks contain steam and they are both connected to a piston/cylinder, as shown in Fig. $\mathrm{P} 6.182$ Initially the piston is at the bottom, and the mass of the piston is such that a pressure of 1.4 MPa below it will be able to lift it. Stream in $A$ is $4 \mathrm{~kg}$ at $7 \mathrm{MPa}$, $700^{\circ} \mathrm{C}$ and $B$ has $2 \mathrm{~kg}$ at $3 \mathrm{MPa}, 350^{\circ} \mathrm{C}$. The two valves are opened, and the water comes to a uniform state. Find the final temperature and the total entropy generation, assuming no heat transfer.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 183

Assume the heat source in Problem 3.217 is at $300^{\circ} \mathrm{C}$ in a setup similar to Fig. $\mathrm{P} 6.182 .$ Find the heat transfer and the entropy generation.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 184

A cylinder fitted with a piston contains $0.5 \mathrm{~kg}$ of R-134a at $60^{\circ} \mathrm{C}$, with a quality of $50 \%$. The $\mathrm{R}-134 \mathrm{a}$ now expands in an internally reversible polytropic process to ambient temperature, $20^{\circ} \mathrm{C}$, at which point the quality is $100 \%$. Any heat transfer is with a constant-temperature source, which is at $60^{\circ} \mathrm{C}$. Find the polytropic exponent $n$ and show that this process satisfies the entropy equation.

Uma Kumari

Numerade Educator

Problem 185

A device brings $2 \mathrm{~kg}$ ammonia from $150 \mathrm{kPa}$ $-20^{\circ} \mathrm{C}$ to $400 \mathrm{kPa}, 80^{\circ} \mathrm{C}$ in a polytropic process.
Find the polytropic exponent $n$, the work, and the heat transfer. Find the total entropy generated, assuming a source at $100^{\circ} \mathrm{C}$.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 186

A rigid tank with $0.5 \mathrm{~kg}$ ammonia at $1600 \mathrm{kPa}$ $160^{\circ} \mathrm{C}$ is cooled in a reversible process by giving heat to a reversible heat engine that has its cold side at ambient temperature, $20^{\circ} \mathrm{C}$, shown in Fig. $\mathrm{P} 6.186 .$ The ammonia eventually reaches $20^{\circ} \mathrm{C}$ and the process stops. Find the heat transfer from the ammonia to the heat engine and the work output of the heat engine.

Uma Kumari

Numerade Educator

Problem 187

A piston/cylinder with constant loading of the piston contains $1 \mathrm{~L}$ water at $400 \mathrm{kPa},$ quality $15 \% .$ It has some stops mounted, so the maximum possible volume is $11 \mathrm{~L}$. A reversible heat pump extracting heat from the ambient at $300 \mathrm{~K}, 100 \mathrm{kPa}$ heats the water to $300^{\circ} \mathrm{C}$. Find the total work and heat transfer for the water and the work input to the heat pump.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 188

An uninsulated cylinder fitted with a piston contains air at $500 \mathrm{kPa}, 200^{\circ} \mathrm{C},$ at which point the volume is $10 \mathrm{~L}$. The external force on the piston is now varied in such a manner that the air expands to $150 \mathrm{kPa}$ $25 \mathrm{~L}$ volume. It is claimed that in this process, the air produces $70 \%$ of the work that would have resulted from a reversible adiabatic expansion from the same initial pressure and temperature to the same final pressure. Room temperature is $20^{\circ} \mathrm{C}$.
a. What is the amount of work claimed?
b. Is this claim possible?

Uma Kumari

Numerade Educator

Problem 189

A small halogen light bulb receives electrical power of $50 \mathrm{~W}$. The small filament is at $1000 \mathrm{~K}$ and gives out $20 \%$ of the power as light and the rest as heat transfer to the gas, which is at $500 \mathrm{~K} ;$ the glass is at $400 \mathrm{~K}$. All the power is absorbed by the room walls at $25^{\circ} \mathrm{C}$. Find the rate of generation of entropy in the filament, in the total bulb including the glass, and in the total room including the bulb.

Uma Kumari

Numerade Educator

Problem 190

Water at 20 psia, 240 F, receives 40 Btu/lbm in a reversible process by heat transfer. Which process changes $s$ the most: constant $T,$ constant $V$ or constant $P ?$

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 191

Saturated water vapor at 20 psia is compressed to 60 psia in a reversible adiabatic process. Find the change in $v$ and $T$

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 192

Consider the steam power plant in Problem $5.133 \mathrm{E}$ and show that this cycle satisfies the inequality of Clausius.

Uma Kumari

Numerade Educator

Problem 193

Find the missing properties of $P, v, s,$ and $x$ for ammonia, $\mathrm{NH}_{3}$.
a. $T=190 \mathrm{~F}, P=100$ psia
b. $T=80 \mathrm{~F}, h=650 \mathrm{Btu} / \mathrm{lbm}$
c. $T=120 \mathrm{~F}, v=1.6117 \mathrm{ft}^{3} / \mathrm{lbm}$

Uma Kumari

Numerade Educator

Problem 194

Find the missing properties and give the phase of the substance
a. $\mathrm{H}_{2} \mathrm{O} \quad \mathrm{s}=1.75 \mathrm{Btu} / \mathrm{lbm} \mathrm{R}, T=150 \mathrm{~F}$ $h=? P=? x=?$
b. $\mathrm{H}_{2} \mathrm{O} \quad u=1350 \mathrm{Btu} / \mathrm{lbm}, P=1500 \mathrm{lbf} / \mathrm{in} .$ $T=? x=? s=?$

Uma Kumari

Numerade Educator

Problem 195

Determine the missing property among $P, T, s,$ and $x$ for $\mathrm{R}-410 \mathrm{a}$ at
a. $T=-20 \mathrm{~F}, v=3.1214 \mathrm{ft}^{3} / \mathrm{lbm}$
b. $T=60 \mathrm{~F}, v=0.3121 \mathrm{ft}^{3} / \mathrm{lbm}$
c. $P=30$ psia, $s=0.3425 \mathrm{Btu} / \mathrm{lbm}-\mathrm{R}$

Uma Kumari

Numerade Educator

Problem 196

In a Carnot engine with water as the working fluid, the high temperature is $500 \mathrm{~F}$ and as $Q_{L}$ is received, the water changes from saturated liquid to saturated vapor. The water pressure at the low temperature is $14.7 \mathrm{lbf} / \mathrm{in.}^{2} .$ Find $T_{L},$ the cycle thermal efficiency, the heat added per pound-mass, and entropy, $s,$ at the beginning of the heat rejection process.

Uma Kumari

Numerade Educator

Problem 197

Consider a Carnot-cycle heat pump with $\mathrm{R}-410 \mathrm{a}$ as the working fluid. Heat is rejected from the R-410a at $110 \mathrm{~F}$, during which process the R-410a changes from saturated vapor to saturated liquid. The heat is transferred to the $\mathrm{R}-410 \mathrm{a}$ at $30 \mathrm{~F}$
a. Show the cycle on a $T-s$ diagram.
b. Find the quality of the $\mathrm{R}-410 \mathrm{a}$ at the beginning and end of the isothermal heat addition process at $30 \mathrm{~F}$
c. Determine the COP for the cycle.

Uma Kumari

Numerade Educator

Problem 198

Do Problem $6.197 \mathrm{E}$ using refrigerant $\mathrm{R}-134 \mathrm{a}$ instead of $\mathrm{R}-410 \mathrm{a}$.

Uma Kumari

Numerade Educator

Problem 199

R-410a at 150 psia and $140 \mathrm{~F}$ is expanded in a piston/cylinder to 75 psia, $80 \mathrm{~F}$ in a reversible process. Find the sign for both the work and the heat transfer for this process.

Uma Kumari

Numerade Educator

Problem 200

A piston/cylinder receives $\mathrm{R}-410 \mathrm{a}$ at 75 psia and compresses it in a reversible adiabatic process to 300 psia, 160 F. Find the initial temperature.

Uma Kumari

Numerade Educator

Problem 201

A piston/cylinder contains 1 lbm water at 40 psia, $600 \mathrm{~F},$ and it now cools to $280 \mathrm{~F}$ in an isobaric process. The heat goes into a heat engine that rejects heat to the ambient at $77 \mathrm{~F}$, shown in Fig. $\mathrm{P} 6.46$, and the whole process is assumed reversible. Find the heat transfer out of the water and the work given out by the heat engine.

Uma Kumari

Numerade Educator

Problem 202

A cylinder fitted with a piston contains ammonia at $120 \mathrm{~F}, 20 \%$ quality with a volume of $60 \mathrm{in} .^{3} .$ The ammonia expands slowly, and during this process heat is transferred to maintain a constant temperature. The process continues until all the liquid is gone. Determine the work and heat transfer for this process.

Uma Kumari

Numerade Educator

Problem 203

A 1 -lb mass of water at $600 \mathrm{~F}$ expands against a piston in a cylinder until it reaches ambient pressure, $14.7 \mathrm{lbf} / \mathrm{in} .^{2},$ at which point the water has a quality of $90 \% .$ It may be assumed that the expansion is reversible and adiabatic.
a. What was the initial pressure in the cylinder?
b. How much work is done by the water?

Uma Kumari

Numerade Educator

Problem 204

A closed tank, $V=0.35 \mathrm{ft}^{3},$ containing $10 \mathrm{lbm}$ water initially at $77 \mathrm{~F}$, is heated to $350 \mathrm{~F}$ by a heat pump that is receiving heat from the surroundings at 77 F. Assume that this process is reversible. Find the heat transfer to the water and the work input to the heat pump.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 206

A rigid, insulated vessel contains superheated vapor steam at $400 \mathrm{lbf} / \mathrm{in} .^{2}, 700 \mathrm{~F}$. A valve on the vessel is opened, allowing steam to escape. It may be assumed that the steam remaining inside the vessel goes through a reversible adiabatic expansion. Determine the fraction of steam that has escaped when the final state inside is saturated vapor.

Uma Kumari

Numerade Educator

Problem 207

Two 5 -lbm blocks of steel, one at $500 \mathrm{~F}$ and the other at $80 \mathrm{~F},$ come in thermal contact. Find the final temperature and the change in the entropy of the steel.

Uma Kumari

Numerade Educator

Problem 208

A foundry form box with $50 \mathrm{lbm}$ of $400 \mathrm{~F}$ hot sand is dumped into a bucket with $2 \mathrm{ft}^{3}$ water at $60 \mathrm{~F}$. Assuming no heat transfer with the surroundings and no boiling away of liquid water, calculate the net entropy change for the masses.

Uma Kumari

Numerade Educator

Problem 209

Heat transfer to a block of 3 lbm ice at $15 \mathrm{~F}$ melts it to liquid at $50 \mathrm{~F}$ in a kitchen. Find the entropy change of the water.

Uma Kumari

Numerade Educator

Problem 210

A rigid tank of 1.2 lbm steel contains 1.5 lbm $\mathrm{R}-134 \mathrm{a}$ at $100 \mathrm{~F}, 80$ psia. The tank is placed in a refrigerator that brings it to $0 \mathrm{~F}$. Find the process heat transfer and the combined steel and $\mathrm{R}-134 \mathrm{a}$ change in entropy.

Uma Kumari

Numerade Educator

Problem 211

A 5-lbm aluminum radiator holds 2 lbm liquid R-134a at $10 \mathrm{~F}$. The setup is brought indoors and heated with 220 Btu. Find the final temperature and the change in entropy of all the mass.

Uma Kumari

Numerade Educator

Problem 212

Four pounds of liquid lead at $750 \mathrm{~F}$ is poured into a form. It then cools at constant pressure down to room temperature at $68 \mathrm{~F}$ as heat is transferred to the room. The melting point of lead is $620 \mathrm{~F}$ and the enthalpy change between the phases $h_{\text {if }}$ is $10.6 \mathrm{Btu} / \mathrm{lbm} .$ The specific heats are found in Table $\mathrm{F} .2$ and $\mathrm{F} .3 .$ Calculate the net entropy change for the lead.

Uma Kumari

Numerade Educator

Problem 213

Air inside a rigid tank is heated from 550 to $600 \mathrm{R}$. Find the entropy increase $s_{2}-s_{1}$. What is the entropy increase if the tank is heated from 2300 to $2350 \mathrm{R} ?$

Uma Kumari

Numerade Educator

Problem 214

$\mathrm{R}-410 \mathrm{a}$ at 60 psia is brought from $60 \mathrm{~F}$ to $240 \mathrm{~F}$ in a constant-pressure process. Evaluate the change in specific entropy using Table $\mathrm{F} .9$ and using ideal gas with $C_{p}=0.1935 \mathrm{Btu} / \mathrm{lbmR}$.

Uma Kumari

Numerade Educator

Problem 215

Oxygen gas in a piston/cylinder at $500 \mathrm{R}$ and 1 atm with a volume of $1 \mathrm{ft}^{3}$ is compressed in a reversible adiabatic process to a final temperature of $1000 \mathrm{R}$. Find the final pressure and volume using constant heat capacity from Table $\mathrm{F} .4$ and repeat with Table $\mathrm{F} .6 .$

Uma Kumari

Numerade Educator

Problem 216

A handheld pump for a bicycle has a volume of 2 in. $^{3}$ when fully extended. You now press the plunger (piston) in while holding your thumb over the exit hole so that an air pressure of $45 \mathrm{lbf} / \mathrm{in} .$ is obtained. The outside atmosphere is at $P_{\mathrm{o}}, T_{\mathrm{o}}$. Consider two cases: (1) it is done quickly $(\sim 1 \mathrm{~s})$ and (2) it is done slowly $(\sim 1 \mathrm{~h})$
a. State the assumptions about the process for each case.
b. Find the final volume and temperature for both cases.

Uma Kumari

Numerade Educator

Problem 217

A piston/cylinder contains air at $2500 \mathrm{R}, 2200$ $\mathrm{lbf} / \mathrm{in} .^{2},$ with $V_{1}=1 \mathrm{in} .^{3}, A_{\mathrm{cyl}}=1 \mathrm{in.}^{2},$ as shown
in Fig. $\mathrm{P} 6.92 .$ The piston is released, and just before the piston exits the end of the cylinder, the pressure inside is $30 \mathrm{lbf} / \mathrm{in} .^{2} .$ If the cylinder is insulated, what is its length? How much work is done by the air inside?

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 218

A $25-\mathrm{ft}^{3}$ insulated, rigid tank contains air at 110 lbf/in. $^{2}, 75$ F. A valve on the tank is opened, and the pressure inside quickly drops to $20 \mathrm{lbf} / \mathrm{in} .^{2}$ at which point the valve is closed. Assuming the air remaining inside has undergone a reversible adiabatic expansion, calculate the mass withdrawn during the process.

Uma Kumari

Numerade Educator

Problem 219

A cylinder/piston contains 0.1 lbm methane gas at 15 psia, 70 F. The gas is compressed reversibly to a pressure of 120 psia. Calculate the work required if the process is adiabatic.

Uma Kumari

Numerade Educator

Problem 220

Helium in a piston/cylinder at $70 \mathrm{~F}, 20$ psia is brought to $720 \mathrm{R}$ in a reversible polytropic process with exponent $n=1.25 .$ You may assume that helium is an ideal gas with constant specific heat. Find the final pressure and both the specific heat transfer and the specific work.

Uma Kumari

Numerade Educator

Problem 221

A cylinder/piston contains air at ambient conditions, $14.7 \mathrm{lbf} / \mathrm{in} .^{2}$ and $70 \mathrm{~F}$ with a volume of $10 \mathrm{ft}^{3} .$ The air is compressed to $100 \mathrm{lbf} / \mathrm{in} .{ }^{2}$ in a reversible polytropic process with exponent $n=1.2,$ after which it is expanded back to $14.7 \mathrm{lbf} / \mathrm{in} .^{2}$ in a reversible adiabatic process.
a. Show the two processes in $P-v$ and $T-s$ diagrams.
b. Determine the final temperature and the net work.

Uma Kumari

Numerade Educator

Problem 222

Consider a heat transfer of 100 Btu from $2400 \mathrm{R}$ hot gases to a steel container at $1200 \mathrm{R}$ that has a heat transfer of the 100 Btu out to some air at $600 \mathrm{R}$. Determine the entropy generation in each of the control volumes indicated in Fig. $\mathrm{P} 6.115$

Uma Kumari

Numerade Educator

Problem 223

A computer chip dissipates 2 Btu of electrical work over time and rejects that as heat transfer from its 125 F surface to $70 \mathrm{~F}$ air. How much entropy is generated in the chip? How much, if any, is generated outside the chip?

Uma Kumari

Numerade Educator

Problem 224

An insulated cylinder/piston contains $\mathrm{R}-134 \mathrm{a}$ at $150 \mathrm{lbf} / \mathrm{in} .^{2}, 120 \mathrm{~F},$ with a volume of $3.5 \mathrm{ft}^{3} .$ The
R-134a expands, moving the piston until the pressure in the cylinder has dropped to $15 \mathrm{lbf} / \mathrm{in} .^{2}$. It is claimed that the $\mathrm{R}-134 \mathrm{a}$ does $180 \mathrm{Btu}$ of work against the piston during the process. Is that possible?

Uma Kumari

Numerade Educator

Problem 225

Heat transfer from a $70 \mathrm{~F}$ kitchen to a block of 3 lbm ice at $15 \mathrm{~F}$ melts it to liquid at $50 \mathrm{~F}$. Find the entropy generation.

Uma Kumari

Numerade Educator

Problem 226

A mass and atmosphere loaded piston/cylinder contains 4 lbm water at $500 \mathrm{lbf} / \mathrm{in.}^{2}, 200 \mathrm{~F}$. Heat is added from a reservoirs at $1200 \mathrm{~F}$ to the water until it reaches $1000 \mathrm{~F}$. Find the work, heat transfer, and total entropy generation for the system and its surroundings.

Uma Kumari

Numerade Educator

Problem 227

A 1 -gal jug of milk at $75 \mathrm{~F}$ is placed in your refrigerator, where it is cooled down to the refrigerator's inside temperature of $40 \mathrm{~F}$. Assume the milk has the properties of liquid water and find the entropy generated in the cooling process.

Uma Kumari

Numerade Educator

Problem 228

A cylinder/piston contains water at $30 \mathrm{lbf} / \mathrm{in} .^{2}$ $400 \mathrm{~F}$ with a volume of $1 \mathrm{ft}^{3}$. The piston is moved slowly, compressing the water to a pressure of $120 \mathrm{lbf} / \mathrm{in} .^{2} .$ The loading on the piston is such that the product $P V$ is a constant. Assuming the room temperature is $70 \mathrm{~F}$, show that this process does not violate the second law.

Uma Kumari

Numerade Educator

Problem 229

A 1 -lb mass of ammonia $\left(\mathrm{NH}_{3}\right)$ is contained in a linear spring-loaded piston/cylinder as saturated liquid at $0 \mathrm{~F}$. Heat is added from a reservoir at $225 \mathrm{~F}$ until a final condition of $200 \mathrm{lbf} / \mathrm{in} .^{2}$
$160 \mathrm{~F}$ is reached. Find the work, heat transfer, and entropy generation, assuming the process is internally reversible.

Uma Kumari

Numerade Educator

Problem 230

A hollow steel sphere with a 2 -ft inside diameter and a 0.1 -in.-thick wall contains water at $300 \mathrm{lbf} / \mathrm{in} .^{2}, 500 \mathrm{~F}$. The system (steel plus water) cools to the ambient temperature, $90 \mathrm{~F}$. Calculate the net entropy change of the system and its surroundings for this process.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 231

One $\mathrm{lbm}$ of air at $540 \mathrm{R}$ is mixed with $2 \mathrm{lbm}$ air at $720 \mathrm{R}$ in a process at a constant 15 psia and $Q=0 .$ Find the final $T$ and the entropy generation in the process.

Uma Kumari

Numerade Educator

Problem 232

One lbm air at 15 psia is mixed with 2 lbm air at 30 psia, both at $540 \mathrm{R}$, in a rigid, insulated tank. Find the final state $(P, T)$ and the entropy generation in the process.

Uma Kumari

Numerade Educator

Problem 233

A rigid container with volume $7 \mathrm{ft}^{3}$ is divided into two equal volumes by a partition. Both sides contain nitrogen; one side is at $300 \mathrm{lbf} / \mathrm{in} .^{2}, 400 \mathrm{~F}$ and the other is at $30 \mathrm{lbf} / \mathrm{in} .^{2}, 200 \mathrm{~F}$. The partition ruptures, and the nitrogen comes to a uniform state at 160 F. Assume the temperature of the surroundings is 68 F. Determine the work done and the entropy generation for the process.

Uma Kumari

Numerade Educator

Problem 234

A constant-pressure piston/cylinder is 2 lbm steel and it contains $1 \mathrm{lbm}$ air at $540 \mathrm{R}, 60$ psia. The system is now heated to $2600 \mathrm{R}$ by a $2800 \mathrm{R}$ source, and the steel has the same temperature as the air. Find the entropy generation using constant specific heats.

Uma Kumari

Numerade Educator

Problem 235

Do Problem $6.234 \mathrm{E}$ using Table F.5.

Uma Kumari

Numerade Educator

Problem 236

Nitrogen at $90 \mathrm{lbf} / \mathrm{in} .^{2}, 260 \mathrm{~F}$ is in a $20 \mathrm{ft}^{3}$ insulated tank connected to pipe with a valve to a second insulated initially empty tank of volume $10 \mathrm{ft}^{3}$. The valve is opened, and the nitrogen fills both tanks. Find the final pressure and temperature and the entropy generation this process causes. Why is the process irreversible?

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 237

A cylinder/piston contains carbon dioxide at 150 lbf/in. $^{2}, 600 \mathrm{~F}$ with a volume of $7 \mathrm{ft}^{3}$. The total external force acting on the piston is proportional to $V^{3}$. This system is allowed to cool to room temperature, $70 \mathrm{~F}$. What is the total entropy generation for the process?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 238

A cylinder/piston contains $4 \mathrm{ft}^{3}$ air at $16 \mathrm{lbf} / \mathrm{in} .^{2}$ $77 \mathrm{~F}$. The air is compressed in a reversible polytropic process to a final state of $120 \mathrm{lbf} / \mathrm{in} .^{2}, 400 \mathrm{~F}$. Assume the heat transfer is with the ambient at $77 \mathrm{~F}$ and determine the polytropic exponent $n$ and the final volume of the air. Find the work done by the air, the heat transfer, and the total entropy generation for the process.

Uma Kumari

Numerade Educator

Problem 239

A room at $72 \mathrm{~F}$ is heated electrically with $1500 \mathrm{~W}$ to keep a steady temperature. The outside ambient air is at $40 \mathrm{~F}$. Find the flux of $S(=\dot{Q} / T)$ into the room air, into the ambient, and the rate of entropy generation.

Uma Kumari

Numerade Educator

Problem 240

A heat pump with $\mathrm{COP}=4$ uses $1 \mathrm{~kW}$ of power input to heat a 78 F room, drawing energy from the outside at $60 \mathrm{~F}$. Assume the high/low temperatures in the heat pump are $120 \mathrm{~F} / 32 \mathrm{~F}$. Find the total rates of entropy into and out of the heat pump, the rate from the outside at $60 \mathrm{~F}$, and the rate to the room at $78 \mathrm{~F}$.

Uma Kumari

Numerade Educator

Problem 241

A window receives $800 \mathrm{Btu} / \mathrm{h}$ of heat transfer at the inside surface of $70 \mathrm{~F}$ and transmits the 800 $\mathrm{Btu} / \mathrm{h}$ from its outside surface at $36 \mathrm{~F},$ continuing to ambient air at $23 \mathrm{~F}$. Find the flux of entropy at all three surfaces and the window's rate of entropy generation.

Uma Kumari

Numerade Educator

Problem 243

A farmer runs a heat pump using 2.5 hp of power input. It keeps a chicken hatchery at a constant $86 \mathrm{~F}$ while the room loses $20 \mathrm{Btu} / \mathrm{s}$ to the colder outside ambient air at $50 \mathrm{~F}$. What is the rate of entropy generated in the heat pump? What is the rate of entropy generated in the heat loss process?

Uma Kumari

Numerade Educator

Problem 244

A cylinder/piston contains 5 lbm water at 80 lbf/in. $^{2}, 1000 \mathrm{~F}$. The piston is restrained by a linear spring so when the system cools down due to heat transfer to the room at $70 \mathrm{~F}$ the water reaches a state of $80 \mathrm{~F}, x=0.05 .$ Calculate the total entropy generation due to this process.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 245

A cylinder/piston contains 5 lbm water at 80 lbf/in. $^{2}, 1000$ F. The piston is restrained by a linear spring so when the system cools down due to heat transfer to the room at $70 \mathrm{~F}$ the water reaches a state of $80 \mathrm{~F}, x=0.05 .$ Calculate the total entropy generation due to this process.

Uma Kumari

Numerade Educator

Problem 246

Write a computer program to solve Problem 6.63 using constant specific heat for both the sand and the liquid water. Let the amount and the initial temperatures be input variables.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 247

Write a program to solve Problem 6.74 with the thermal storage rock bed in Problem $5.60 .$ Let the size and temperatures be input variables so that the heat engine work output can be studied as a function of the system parameters.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 248

Write a program to solve the following problem. One of the gases listed in Table $A .6$ undergoes a reversible adiabatic process in a cylinder from $P_{1}, T_{1}$ to $P_{2} .$ We wish to calculate the final temperature and the work for the process by three methods:
a. Integrating the specific heat equation.
b. Assuming constant specific heat at temperature, $T_{1}$
c. Assuming constant specific heat at the average temperature (by iteration).

Manik Pulyani

Numerade Educator

Problem 249

Write a program to solve a problem similar to Problem $6.103,$ but instead of the ideal gas tables, use the formula for the specific heat as a function of temperature in Table A.6.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 250

Write a program to study a general polytropic process in an ideal gas with constant specific heat. Take Problem 6.110 as an example.

Prem Bijarniya

Numerade Educator

Problem 251

Write a program to solve the general case of Problem 6.111 , in which the initial state and the expansion ratio are input variables.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 252

A piston/cylinder maintaining constant pressure contains $0.5 \mathrm{~kg}$ water at room temperature, $20^{\circ} \mathrm{C}$, $100 \mathrm{kPa} .$ An electric heater of $500 \mathrm{~W}$ heats the water to $500^{\circ} \mathrm{C}$. Assume no heat losses to the ambient air and plot the temperature and total accumulated entropy production as a function of time. Investigate the first part of the process, namely, bringing the water to the boiling point, by measuring it in your kitchen and knowing the rate of power added.

Uma Kumari

Numerade Educator

Problem 253

Air in a piston/cylinder is used as a small air spring that should support a steady load of $200 \mathrm{~N}$. Assume that the load can vary with $\pm 10 \%$ over a period of $1 \mathrm{~s}$ and that the displacement should be limited to $\pm 0.01 \mathrm{~m} .$ For some choice of sizes, show the spring displacement, $x,$ as a function of load and compare that to an elastic linear coil spring designed for the same conditions.

Susan Hallstrom

Susan Hallstrom

Numerade Educator