Fundamentals of Thermodynamics

Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen

Chapter 4 Work and Heat - all with Video Answers

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Chapter Questions

00:52

Problem 1

The electric company charges the customers per kilowatt-hour. What is that in SI units?

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00:58

Problem 2

A car engine is rated at 160 hp. What is the power in SI units?

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01:36

Problem 3

A 1200 -hp dragster engine has a drive shaft rotating at 2000 RPM. How much torque is on the shaft?

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01:21

Problem 4

A 1200 -hp dragster engine drives the car with a speed of $100 \mathrm{km} / \mathrm{h}$. How much force is between the tires and the road?

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01:13

Two hydraulic piston/cylinders are connected through a hydraulic line so that they have roughly the same pressure. If they have diameters of $D_{1}$ and $D_{2}=2 D_{1}$ respectively, what can you say about the piston forces $F_{1}$ and $F_{2} ?$

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01:07

Problem 6

Normally pistons have a flat head, but in diesel engines pistons can have bowls in them and protruding ridges. Does this geometry influence the work term?

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00:47

Problem 7

What is roughly the relative magnitude of the work in the process $1-2 c$ versus the process $1-2 a$ shown in Fig. $4.8 ?$

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01:28

Problem 8

A hydraulic cylinder of area $0.01 \mathrm{m}^{2}$ must push a $1000-\mathrm{kg}$ arm and shovel $0.5 \mathrm{m}$ straight up. What pressure is needed and how much work is done?

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01:03

Problem 9

A work of $2.5 \mathrm{kJ}$ must be delivered on a rod from a pneumatic piston/cylinder where the air pressure is limited to 500 kPa. What diameter cylinder should I have to restrict the rod motion to maximum $0.5 \mathrm{m} ?$

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00:49

Problem 10

Helium gas expands from $125 \mathrm{kPa}, 350 \mathrm{K},$ and $0.25 \mathrm{m}^{3}$ to $100 \mathrm{kPa}$ in a polytropic process with $n=1.667 .$ Is the work positive, negative, or zero?

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02:27

Problem 11

An ideal gas goes through an expansion process whereby the volume doubles. Which process will lead to the larger work output, an isothermal process or a polytropic process with $n=1.25 ?$

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01:01

Problem 12

Show how the polytropic exponent $n$ can be evaluated if you know the end state properties, $\left(P_{1}, V_{i}\right)$ and $\left(P_{2}, V_{2}\right)$.

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00:53

Problem 13

A drag force on an object moving through a medium (like a car through air or a submarine through water) is $F_{d}=0.225 \mathrm{ApV}^{2}$. Verify that the unit become newtons.

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01:00

Problem 14

A force of $1.2 \mathrm{kN}$ moves a truck with $60 \mathrm{km} / \mathrm{h}$ up a hill. What is the power?

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01:02

Problem 15

Electric power is volts times amperes $(P=V i)$ When a car battery at $12 \mathrm{V}$ is charged with $6 \mathrm{A}$ for $3 \mathrm{h}$, how much energy is delivered?

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00:38

Problem 16

Torque and energy and work have the same units $(\mathrm{N} \mathrm{m}) .$ Explain the difference.

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00:44

Problem 17

Find the rate of conduction heat transfer through a 1.5-cm-thick hardwood board, $k=0.16 \mathrm{W} / \mathrm{m} \mathrm{K}$ with a temperature difference between the two sides of $20^{\circ} \mathrm{C}$

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00:49

Problem 18

A $2-\mathrm{m}^{2}$ window has a surface temperature of $15^{\circ} \mathrm{C}$ and the outside wind is blowing air at $2^{\circ} \mathrm{C}$ across it with a convection heat transfer coefficient of $h=$ $125 \mathrm{W} / \mathrm{m}^{2} \mathrm{K}$. What is the total heat transfer loss?

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00:58

Problem 19

A radiant heating lamp has a surface temperature of $1000 \mathrm{K}$ with $\varepsilon=0.8 .$ How large a surface area is needed to provide $250 \mathrm{W}$ of radiation heat transfer?

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00:54

Problem 20

A piston of mass $2 \mathrm{kg}$ is lowered $0.5 \mathrm{m}$ in the standard gravitational field. Find the required force and the work involved in the process.

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01:08

Problem 21

An escalator raises a 100 -kg bucket of sand $10 \mathrm{m}$ in 1 min. Determine the total amount of work done during the process.

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01:17

Problem 22

A bulldozer pushes $500 \mathrm{kg}$ of dirt $100 \mathrm{m}$ with a force of $1500 \mathrm{N}$. It then lifts the dirt $3 \mathrm{m}$ up to put it in a dump truck. How much work did it do in each situation?

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01:11

Problem 23

A hydraulic cylinder has a piston of cross-sectional area $25 \mathrm{cm}^{2}$ and a fluid pressure of 2 MPa. If the piston is moved $0.25 \mathrm{m}$, how much work is done?

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01:26

Problem 24

Two hydraulic cylinders maintain a pressure of $1200 \mathrm{kPa} .$ One has a cross-sectional area of 0.01 $\mathrm{m}^{2},$ the other one of $0.03 \mathrm{m}^{2} .$ To deliver $1 \mathrm{kJ}$ of work to the piston, how large a displacement ( $V$ ) and piston motion $H$ are needed for each cylinder? Neglect $P_{\text {atn" }}$

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01:11

Problem 25

A linear spring, $F=k_{s}\left(x-x_{0}\right)$ with spring constant $k_{s}=500 \mathrm{N} / \mathrm{m}$ is stretched until it is $100 \mathrm{mm}$ longer. Find the required force and the vork input.

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00:42

Problem 26

A nonlinear spring has a force versus the displacement relation of $F=k_{s}\left(x-x_{0}\right)^{n}$. If the spring end is moved to $x_{1}$ from the relaxed state, determine the formula for the required work.

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01:14

Problem 27

The rolling resistance of a car depends on its weight as $F=0.006 \mathrm{mg}$. How long will a car of $1400 \mathrm{kg}$ drive for a work input of $25 \mathrm{kJ} ?$

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01:28

Problem 28

A car drives for half an hour at constant speed and uses 30 MJ over a distance of $40 \mathrm{km}$. What was the traction force to the road and its speed?

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02:15

Problem 29

The air drag force on a car is $0.225 \mathrm{ApV}^{2}$. Assume air at $290 \mathrm{K}, 100 \mathrm{kPa}$ and a car frontal area of $4 \mathrm{m}^{2}$ driving at $90 \mathrm{km} / \mathrm{h}$. How much energy is used to overcome the air drag driving for 30 min?

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03:07

Problem 30

Two hydraulic piston/cylinders are connected with a line. The master cylinder has an area of $5 \mathrm{cm}^{2}$, creating a pressure of $1000 \mathrm{kPa}$. The slave cylinder has an area of $3 \mathrm{cm}^{2}$. If $25 \mathrm{J}$ is the work input to the master cylinder, what is the force and displacement of each piston and the work output of the slave cylinder piston?

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01:51

Problem 31

A constant-pressure piston/cylinder assembly contains $0.2 \mathrm{kg}$ of water as saturated vapor at $400 \mathrm{kPa}$. It is now cooled so that the water occupies half the original volume. Find the work done in the
process.

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01:57

Problem 32

A steam radiator in a room at $25^{\circ} \mathrm{C}$ has saturated water vapor at $110 \mathrm{kPa}$ flowing through it when the inlet and exit valves are closed. What are the pressure and the quality of the water when it has cooled to $25^{\circ} \mathrm{C} ?$ How much work is done?

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01:51

Problem 33

A $400-\mathrm{L}$ tank, $A$ (see Fig. $\mathrm{P} 4.33$ ), contains argon gas at $250 \mathrm{kPa}$ and $30^{\circ} \mathrm{C}$. Cylinder $B$, having a frictionless piston of such mass that a pressure of 150 kPa will float it, is initially empty. The valve is opened and argon flows into $B$ and eventually reaches a uniform state of $150 \mathrm{kPa}$ and $30^{\circ} \mathrm{C}$ throughout. What is the work done by the argon?

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02:32

Problem 34

A piston/cylinder contains air at $600 \mathrm{kPa}, 290 \mathrm{K}$ and a volume of $0.01 \mathrm{m}^{3} .$ A constant-pressure process gives $54 \mathrm{kJ}$ of work out. Find the final volume and temperature of the air.

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01:54

Problem 35

Saturated water vapor at $200 \mathrm{kPa}$ is in a constantpressure piston/cylinder. In this state, the piston is $0.1 \mathrm{m}$ from the cylinder bottom and the cylinder area is $0.25 \mathrm{m}^{2}$. The temperature is then changed to $200^{\circ} \mathrm{C} .$ Find the work in the process.

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01:51

Problem 36

A cylinder fitted with a frictionless piston contains $5 \mathrm{kg}$ of superheated refrigerant $\mathrm{R}-134 \mathrm{a}$ vapor at $1000 \mathrm{kPa}$ and $140^{\circ} \mathrm{C} .$ The setup is cooled at constant pressure until the $\mathrm{R}-134 \mathrm{a}$ reaches a quality of $25 \%$. Calculate the work done in the process.

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01:14

Problem 37

Find the specific work in Problem 3.54 for the case where the volume is reduced.

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01:30

Problem 38

A piston/cylinder has $5 \mathrm{m}$ of liquid $20^{\circ} \mathrm{C}$ water on top of the piston $(m=0)$ with cross-sectional area of $0.1 \mathrm{m}^{2},$ see Fig. $\mathrm{P} 2.57 .$ Air is let in under the piston that rises and pushes the water out over the top edge, Find the necessary work to push all the water out and plot the process in a $P-V$ diagram.

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01:25

Problem 39

Air in a spring-loaded piston/cylinder setup has a pressure that is linear with volume, $P=A+B V$ With an initial state of $P=150 \mathrm{kPa}, V=1 \mathrm{L}$ and a final state of $800 \mathrm{kPa}$ and volume $1.5 \mathrm{L}$, it is similar to the setup in Problem 3.113 . Find the work done by the air.

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02:32

Problem 40

Find the specific work in Problem 3.43

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02:45

Problem 41

A piston/cylinder contains 1 kg of water at $20^{\circ} \mathrm{C}$ with volume $0.1 \mathrm{m}^{3} .$ By mistake someone locks the piston, preventing it from moving while we heat the water to saturated vapor. Find the final temperature and volume, and the process work.

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04:36

Problem 42

A piston/cylinder assembly contains 1 kg of liquid water at $20^{\circ} \mathrm{C}$ and $300 \mathrm{kPa}$, as shown in Fig. P4.42. There is a linear spring mounted on the piston such that when the water is heated the pressure reaches
$3 \mathrm{MPa}$ with a volume of $0.1 \mathrm{m}^{3}$
a. Find the final temperature.
b. Plot the process in a $P$ -v diagram.
c. Find the work in the process.

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01:41

Problem 43

A piston/cylinder assembly contains $3 \mathrm{kg}$ of air at $20^{\circ} \mathrm{C}$ and $300 \mathrm{kPa}$. It is now heated in a constant pressure process to $600 \mathrm{K}$
a. Find the final volume.
b. Plot the process path in a $P--v$ diagram.
c. Find the work in the process.

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01:36

Problem 44

A piston/cylinder assembly contains $0.5 \mathrm{kg}$ of air at $500 \mathrm{kPa}$ and $500 \mathrm{K}$. The air expands in a process such that $P$ is linearly decreasing with volume to a final state of $100 \mathrm{kPa}, 300 \mathrm{K}$. Find the work in the
process.

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03:33

Problem 45

Consider the nonequilibrium process described in Problem $3.109 .$ Determine the work done by the carbon dioxide in the cylinder during the process.

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04:28

Problem 46

Consider the problem of inflating the helium balloon, as described in Problem $3.79 .$ For a control volume that consists of the helium inside the balloon determine the work done during the filling process when the diameter changes from $1 \mathrm{m}$ to $4 \mathrm{m}$

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02:58

Problem 47

Consider a mass going through a polytropic process where pressure is directly proportional to volume $(n=-1) .$ The process starts with $P=0$ $V=0$ and ends with $P=600 \mathrm{kPa}, V=0.01 \mathrm{m}^{3}$
Find the boundary work done by the mass.

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01:47

Problem 48

The piston/cylinder arrangement shown in Fig. P4.48 contains carbon dioxide at $300 \mathrm{KPa}$ and $100^{\circ} \mathrm{C}$ with a volume of $0.2 \mathrm{m}^{3} .$ Weights are added to the piston such that the gas compresses according to the relation $P V^{12}=$ constant to a final temperature of $200^{\circ} \mathrm{C}$ Determine the work done during the process.

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01:28

Problem 49

A gas initially at $1 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$ is contained in a piston and cylinder arrangement with an initial volume of $0.1 \mathrm{m}^{3}$. The gas is then slowly expanded according to the relation $P V=$ constant until a final pressure of $100 \mathrm{kPa}$ is reached. Determine the work for this process.

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01:33

Problem 50

Helium gas expands from $125 \mathrm{kPa}, 350 \mathrm{K},$ and $0.25 \mathrm{m}^{3}$ to $100 \mathrm{kPa}$ in a polytropic process with $n=1.667 .$ How much work does it give out?

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02:53

Problem 51

Air goes through a polytropic process from $125 \mathrm{kPa}$ and $325 \mathrm{K}$ to $300 \mathrm{kPa}$ and $500 \mathrm{K}$. Find the polytropic exponent $n$ and the specific work in the process.

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01:39

Problem 52

A piston/cylinder device contains $0.1 \mathrm{kg}$ of air at 100 $\mathrm{kPa}$ and $400 \mathrm{K}$ that goes through a polytropic compression process with $n=1.3$ to a pressure of 300
process?

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01:37

Problem 53

A balloon behaves so the pressure is $P=C_{2} V^{1 / 3}$ $C_{2}=100 \mathrm{kPa} / \mathrm{m} .$ The balloon is blown up with air from a starting volume of $1 \mathrm{m}^{3}$ to a volume of $3 \mathrm{m}^{3} .$ Find the final mass of the air, assuming it is at $25^{\circ} \mathrm{C},$ and the work done by the air.

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02:15

Problem 54

A balloon behaves such that the pressure inside is proportional to the diameter squared. It contains $2 \mathrm{kg}$ of ammonia at $0^{\circ} \mathrm{C},$ with $60 \%$ quality. The balloon and ammonia are now heated so that a final pressure of $600 \mathrm{kPa}$ is reached. Considering the ammonia as a control mass, find the amount of work done in the process.

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02:45

Problem 55

Consider a piston/cylinder setup with 0.5 kg of R-134a as saturated vapor at $-10^{\circ} \mathrm{C}$. It is now compressed to a pressure of $500 \mathrm{kPa}$ in a polytropic process with $n=1.5 .$ Find the final volume and temperature, and determine the work done during the process.

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03:15

Problem 56

Consider the process described in Problem 3.98 With $1 \mathrm{kg}$ of water as a control mass, determine the boundary work during the process.

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02:06

Problem 57

Find the work done in Problem 3.106

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03:57

Problem 58

A piston/cylinder contains water at $500^{\circ} \mathrm{C}, 3 \mathrm{MPa}$ It is cooled in a polytropic process to $200^{\circ} \mathrm{C}$
1 MPa. Find the polytropic exponent and the specific work in the process.

Vipender Yadav

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01:11

Problem 59

Consider a two-part process with an expansion from 0.1 to $0.2 \mathrm{m}^{3}$ at a constant pressure of 150 kPa followed by an expansion from 0.2 to $0.4 \mathrm{m}^{3}$ with a linearly rising pressure from $150 \mathrm{kPa}$ ending at $300 \mathrm{kPa}$. Show the process in a $P-V$ diagram and find the boundary work.

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03:07

Problem 60

A cylinder containing $1 \mathrm{kg}$ of ammonia has an externally loaded piston. Initially the ammonia is at 2 MPa and $180^{\circ} \mathrm{C}$. It is now cooled to saturated vapor at $40^{\circ} \mathrm{C}$ and then further cooled to $20^{\circ} \mathrm{C}$, at which point the quality is $50 \%$. Find the total work for the process, assuming a piecewise linear variation of $P$ versus $V$

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02:38

Problem 61

A piston/cylinder arrangement shown in Fig. $\mathrm{P} 4.61$ initially contains air at $150 \mathrm{kPa}$ and $400^{\circ} \mathrm{C}$. The setup is allowed to cool to the ambient temperature of $20^{\circ} \mathrm{C}$
a. Is the piston resting on the stops in the final state? What is the final pressure in the cylinder?
b. What is the specific work done by the air during the process?

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02:25

Problem 62

A piston/cylinder has $1.5 \mathrm{kg}$ of air at $300 \mathrm{K}$ and 150 $\mathrm{kPa} .$ It is now heated up in a two step process. First constant volume to $1000 \mathrm{K}$ (state 2 ) then followed by a constant pressure process to $1500 \mathrm{K}$, state 3 . Find the final volume and the work in the process.

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02:10

Problem 63

A piston/cylinder assembly (Fig. P4.63) has I kg of $R-134 a$ at state 1 with $110^{\circ} \mathrm{C}, 600 \mathrm{kPa}$. It is then brought to saturated vapor, state $2,$ by cooling while the piston is locked with a pin. Now the piston is balanced with an additional constant force and the pin is removed. The cooling continues to a state $3,$ where the $R-134$ a is saturated liquid. Show the processes in a $P-V$ diagram and find the work in each of the two steps, 1 to 2 and 2 to 3.

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02:28

Problem 64

The refrigerant $R-22$ is contained in a piston cylinder as shown in Fig. P4.64, where the volume is 11 L when the piston hits the stops. The initial state is $-30^{\circ} \mathrm{C}, 150 \mathrm{kPa}$, with a volume of $10 \mathrm{L}$. This sys tem is brought indoors and warms up to $15^{\circ} \mathrm{C}$.
a. Is the piston at the stops in the final state?
b. Find the work done by the R-22 during this process.

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02:14

Problem 65

A piston/cylinder assembly contains $50 \mathrm{kg}$ of water at $200 \mathrm{kPa}$ with a volume of $0.1 \mathrm{m}^{3} .$ Stops in the cylinder restrict the enclosed volume to $0.5 \mathrm{m}^{3}$ similar to the setup in Problem 4.64 . The water is now heated to $200^{\circ} \mathrm{C}$. Find the final pressure, volume, and work done by the water.

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01:22

Problem 66

Find the work in Problem 3,108 ,

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02:44

Problem 67

A piston/cylinder assembly contains 1 kg of liquid water at $20^{\circ} \mathrm{C}$ and 300 kPa. Initially the piston floats, similar to the setup in Problem $4.64,$ with a maximum enclosed volume of $0.002 \mathrm{m}^{3}$ if the piston touches the stops. Now heat is added so that a final pressure of $600 \mathrm{kPa}$ is reached. Find the final volume and the work in the process.

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02:24

Problem 68

Ten kilograms of water in a piston/cylinder arrangement exist as saturated liquid/vapor at $100 \mathrm{kPa}$, with a quality of $50 \%$. It is now heated so the volume triples. The mass of the piston is such that a cylinder pressure of $200 \mathrm{kPa}$ will float it (see Fig. P4.68).
a. Find the final temperature and volume of the water.
b. Find the work given out by the water.

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02:52

Problem 69

Find the work in Problem 3.63

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02:31

Problem 70

A piston/cylinder setup similar to Problem 4.68 contains $0.1 \mathrm{kg}$ saturated liquid and vapor water at $100 \mathrm{kPa}$ with quality $25 \% .$ The mass of the piston is such that a pressure of $500 \mathrm{kPa}$ will float it. The water is heated to $300^{\circ} \mathrm{C}$. Find the final pressure, volume, and work, $_{1} W_{2}$

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01:08

Problem 71

A 0.5 -m-long steel rod with a 1 -cm diameter is stretched in a tensile test. What is the work required to obtain a relative strain of $0.1 \%$ ? The modulus of elasticity of steel is $2 \times 10^{8} \mathrm{kPa}$

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02:06

Problem 72

A copper wire of diameter $2 \mathrm{mm}$ is $10 \mathrm{m}$ long and stretched out between two posts. The normal stress (pressure) $\sigma=E\left(L-L_{0}\right) / L_{0},$ depends on the length $L$ versus the unstretched length $L_{0}$ and Young's modulus $E=1.1 \times 10^{6} \mathrm{kPa}$. The force is $F=A \sigma$ and measured to be $110 \mathrm{N}$. How much longer is the wire and how much work was put in?

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00:49

Problem 73

A film of ethanol at $20^{\circ} \mathrm{C}$ has a surface tension of $22.3 \mathrm{mN} / \mathrm{m}$ and is maintained on a wire frame as shown in Fig. P4.73. Consider the film with two surfaces as a control mass and find the work done when the wire is moved $10 \mathrm{mm}$ to make the film $20 \times 40 \mathrm{mm}$

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00:54

Problem 74

Assume a balloon material with a constant surface tension of $\mathscr{S}=2 \mathrm{N} / \mathrm{m}$. What is the work required to stretch a special balloon up to a radius of $r=0.5 \mathrm{m} ?$ Neglect any effect from atmospheric pressure.

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01:14

Problem 75

A soap bubble has a surface tension of $\mathscr{S}=3 \times 10^{-4}$ $\mathrm{N} / \mathrm{cm}$ as it sits flat on a rigid ring of diameter $5 \mathrm{cm}$ You now blow on the film to create a half-sphere surface of diameter $5 \mathrm{cm} .$ How much work was done?

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01:35

Problem 76

Assume we fill a spherical balloon from a bottle of helium gas. The helium gas provides work $\int P d V$ that stretches the balloon material $\int S d A$ and pushes back the atmosphere $\int P_{0} d V$. Write the in cremental balance for $d W_{\text {heliom }}=d W_{\text {stretch }}+d W_{\text {atm }}$ to establish the connection between the helium pressure, the surface tension $S,$ and $P_{0}$ as a function of radius.

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01:26

Problem 77

A sheet of rubber is stretched out over a ring of ra$\operatorname{dius} 0.25 \mathrm{m} .$ I pour liquid water at $20^{\circ} \mathrm{C}$ on it, as in Fig. $\mathrm{P} 4.77,$ so that the rubber forms a half sphere (cup). Neglect the rubber mass and find the surface tension near the ring.

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01:16

Problem 78

Consider a window-mounted air-conditioning unit used in the summer to cool incoming air. Examine the system boundaries for rates of work and heat transfer, including signs.

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01:56

Problem 79

Consider a hot-air heating system for a home. Examine the following systems for heat transfer.
a. The combustion chamber and combustion gas side of the heat transfer area
b. The furnace as a whole, including the hot- and cold-air ducts and chimney

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03:31

Problem 80

Consider a household refirgerator that has just been filled up with room-temperature food. Define a control volume (mass) and examine its boundaries for rates of work and heat transfer, including sign.
a. Immediately after the food is placed in the refrigerator
b. After a long period of time has elapsed and the food is cold

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01:25

Problem 81

A room is heated with an electric space heater on a winter day. Examine the following control volumes, regarding heat transfer and work, including sign:
a. The space heater
b. Room
c. The space heater and the room together

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01:01

Problem 82

An escalator raises a 100 -kg bucket $10 \mathrm{m}$ in $1 \mathrm{min}$. Determine the rate of work in the process.

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01:25

Problem 83

A car uses 25 hp to drive at a horizontal level at a constant speed of $100 \mathrm{km} / \mathrm{h}$. What is the traction force between the tires and the road?

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02:24

Problem 84

A piston/cylinder of cross-sectional area $0.01 \mathrm{m}^{2}$ maintains constant pressure. It contains $1 \mathrm{kg}$ of water with a quality of $5 \%$ at $150^{\circ} \mathrm{C}$. If we heat so that $1 \mathrm{g} / \mathrm{s}$ of liquid turns into vapor, what is the rate of work out?

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00:43

Problem 85

A crane lifts a bucket of cement with a total mass of $450 \mathrm{kg}$ vertically upward with a constant velocity of $2 \mathrm{m} / \mathrm{s} .$ Find the rate of work needed to do this.

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00:56

Problem 86

Consider the car with the rolling resistance as in Problem $4.27 .$ How fast can it drive using 30 hp?

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01:56

Problem 87

Consider the car with the air drag force as in Problem $4.29 .$ How fast can it drive using $30 \mathrm{hp} ?$

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02:38

Problem 88

Consider a 1400 -kg car having rolling resistance as in Problem 4.27 and air resistance as in Problem 4.29. How fast can it drive using 30 hp?

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01:13

Problem 89

A battery is well insulated while being charged by $12.3 \mathrm{V}$ at a current of $6 \mathrm{A}$. Take the battery as a control mass and find the instantaneous rate of work and the total work done over $4 \mathrm{h}$.

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00:25

Problem 90

A current of 10 A runs through a resistor with a resistance of $15 \Omega .$ Find the rate of work that heats the resistor up.

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01:02

Problem 91

A pressure of $650 \mathrm{kPa}$ pushes a piston of diameter $0.25 \mathrm{m}$ with $\mathrm{V}=5 \mathrm{m} / \mathrm{s}$. What is the volume displacement rate, the force, and the transmitted power?

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00:44

Problem 92

Assume the process in Problem 4.59 takes place with a constant rate of change in volume over 2 minutes. Show the power (rate of work) as a function of time.

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01:09

Problem 93

Air at a constant pressure in a piston/cylinder is at $300 \mathrm{kPa}, 300 \mathrm{K}$ and has a volume of $0.1 \mathrm{m}^{3} .$ It is heated to $600 \mathrm{K}$ over $30 \mathrm{s}$ in a process with constant piston velocity. Find the power delivered to the piston.

Sanjeev Kumar

Numerade Educator

00:52

Problem 94

A torque of $650 \mathrm{N} \mathrm{m}$ rotates a shaft of diameter $0.25 \mathrm{m}$ with $\omega=50 \mathrm{rad} / \mathrm{s} .$ What is the shaft surface speed and the transmitted power?

Sanjeev Kumar

Numerade Educator

00:30

Problem 95

The sun shines on a $150-\mathrm{m}^{2}$ road surface so that it is at $45^{\circ} \mathrm{C}$. Below the 5 -cm-thick asphalt, with average conductivity of $0.06 \mathrm{W} / \mathrm{m} \mathrm{K},$ is a layer of compacted nubble at a temperature of $15^{\circ} \mathrm{C}$. Find the rate of heat transfer to the rubble.

Sanjeev Kumar

Numerade Educator

00:57

Problem 96

A steel pot, with conductivity of $50 \mathrm{W} / \mathrm{m}$ K and a 5-mm-thick bottom, is filled with 15 'C liquid water. The pot has a diameter of $20 \mathrm{cm}$ and is now placed on an electric stove that delivers $250 \mathrm{W}$ as heat transfer. Find the temperature on the outer pot bot tom surface assuming the inner surface is at $15^{\circ} \mathrm{C}$.

Sanjeev Kumar

Numerade Educator

01:00

Problem 97

A water heater is covered up with insulation boards over a total surface area of $3 \mathrm{m}^{2}$. The inside board surface is at $75^{\circ} \mathrm{C}$, the outside surface is at $20^{\circ} \mathrm{C}$, and the board material has a conductivity of $0.08 \mathrm{W} / \mathrm{m}$ K. How thick should the board be to limit the heat transfer loss to $200 \mathrm{W} ?$

Sanjeev Kumar

Numerade Educator

01:44

Problem 98

You drive a car on a winter day with the atmospheric air at $-15^{\circ} \mathrm{C}$, and you keep the outside front windshield surface temperature at $+2^{\circ} \mathrm{C}$ by blowing hot air on the inside surface. If the windshield is $0.5 \mathrm{m}^{2}$ and the outside convection coefficient is $250 \mathrm{W} / \mathrm{m}^{2} \mathrm{K},$ find the rate of energy loss through the front windshield. For that heat transfer rate and a 5 -mm-thick glass with $k=1.25 \mathrm{W} / \mathrm{m} \mathrm{K}$, what is then the inside windshield surface temperature?

Sanjeev Kumar

Numerade Educator

00:52

Problem 99

A large condenser (heat exchanger) in a power plant must transfer a total of $100 \mathrm{MW}$ from steam running in a pipe to seawater being pumped through the heat exchanger. Assume the wall separating the steam and 'seawater is $4 \mathrm{mm}$ of steel, with conductivity of $15 \mathrm{W} / \mathrm{m} \mathrm{K},$ and that a maximum of $5^{\circ} \mathrm{C}$ -difference between the two fluids is allowed in the design. Find the required minimum area for the heat transfer, neglecting any convective heat transfer in the flows.

Sanjeev Kumar

Numerade Educator

00:51

Problem 100

The black grille on the back of a refrigerator has a surface temperature of $35^{\circ} \mathrm{C}$ with a total surface area of $1 \mathrm{m}^{2} .$ Heat transfer to the room air at $20^{\circ} \mathrm{C}$ takes place with an average convective heat transfer coefficient of $15 \mathrm{W} / \mathrm{m}^{2} \mathrm{K} .$ How much energy can be removed during 15 minutes of operation?

Sanjeev Kumar

Numerade Educator

00:59

Problem 101

Owing to a faulty door contact, the small light bulb (25 W) inside a refrigerator is kept on and limited insulation lets $50 \mathrm{W}$ of energy from the outside seep into the refrigerated space. How much of a temperature difference to the ambient surroundings at $20^{\circ} \mathrm{C}$ must the refrigerator have in its heat exchanger with an area of $1 \mathrm{m}^{2}$ and an average heat transfer coefficient of $15 \mathrm{W} / \mathrm{m}^{2} \mathrm{K}$ to reject the leaks of energy?

Sanjeev Kumar

Numerade Educator

00:45

Problem 102

The brake shoe and steel drum of a car continuously absorb $25 \mathrm{W}$ as the car slows down. Assume a total outside surface area of $0.1 \mathrm{m}^{2}$ with a convective heat transfer coefficient of $10 \mathrm{W} / \mathrm{m}^{2} \mathrm{K}$ to the air at $20^{\circ} \mathrm{C}$. How hot does the outside brake and drum surface become when steady conditions are reached?

Sanjeev Kumar

Numerade Educator

05:04

Problem 103

A wall surface on a house is $30^{\circ} \mathrm{C}$ with an emissivity of $\varepsilon=0.7 .$ The surrounding ambient air is at $15^{\circ} \mathrm{C}$ with an average emissivity of $0.9 .$ Find the rate of radiation energy from each of those surfaces per unit area.

Shahab Ullah

Numerade Educator

00:42

Problem 104

A log of burning wood in the fireplace has a surface temperature of $450^{\circ} \mathrm{C}$. Assume the emissivity is 1 (perfect black body) and find the radiant emission of energy per unit surface area.

Sanjeev Kumar

Numerade Educator

01:13

Problem 105

A radiant heat lamp is a rod, $0.5 \mathrm{m}$ long and 0.5 $\mathrm{cm}$ in diameter, through which $400 \mathrm{W}$ of electric energy is deposited. Assume the surface has an emissivity of 0.9 and neglect incoming radiation. What will the rod surface temperature be?

Sanjeev Kumar

Numerade Educator

02:34

Problem 106

A vertical cylinder (Fig. P4.106) has a $61.18 \mathrm{kg}$ piston locked with a pin, trapping $10 \mathrm{L}$ of $\mathrm{R}-22$ at $10^{\circ} \mathrm{C}$ with $90 \%$ quality inside. Atmospheric pressure is $100 \mathrm{kPa}$, and the cylinder cross-sectional area is $0.006 \mathrm{m}^{2}$. The pin is removed, alloving the piston to move and come to rest with a final temperature of $10^{\circ} \mathrm{C}$ for the $\mathrm{R}-22 .$ Find the final pressure, final volume, and work done by the R-22.

Sanjeev Kumar

Numerade Educator

02:33

Problem 107

A piston/cylinder assembly contains butane, $\mathrm{C}_{4} \mathrm{H}_{10},$ at $300^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$ with a volume of
$0.02 \mathrm{m}^{3} .$ The gas is now compressed slowly in an isothermal process to $300 \mathrm{kPa}$
a. Show that it is reasonable to assume that butane behaves as an ideal gas during this process.
b. Determine the work done by the butane during the process.

Sanjeev Kumar

Numerade Educator

02:28

Problem 108

A cylinder fitted with a piston contains propane gas at $100 \mathrm{kPa}$ and $300 \mathrm{K}$ with a volume of 0.2 $\mathrm{m}^{3} .$ The gas is now slowly compressed according to the relation $P V^{\mathrm{l} .1}=$ constant to a final temperature of $340 \mathrm{K}$. Justify the use of the ideal-gas model. Find the final pressure and the work done during the process.

Sanjeev Kumar

Numerade Educator

02:26

Problem 109

The gas space above the water in a closed storage tank contains nitrogen at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$. Total tank volume is $4 \mathrm{m}^{3},$ and there is $500 \mathrm{kg}$ of water at $25^{\circ} \mathrm{C} .$ An additional $500 \mathrm{kg}$ of water is now forced into the tank. Assuming constant temperature throughout, find the final pressure of the nitrogen and the work done on the nitrogen in this process.

Sanjeev Kumar

Numerade Educator

02:18

Problem 110

Two kilograms of water are contained in a piston/cylinder (Fig. P4.110) with a massless piston loaded with a linear spring and the outside atmosphere. Initially the spring force is zero and $P_{1}=$ $P_{0}=100 \mathrm{kPa}$ with a volume of $0.2 \mathrm{m}^{3} .$ If the piston just hits the upper stops, the volume is $0.8 \mathrm{m}^{3}$ and $T=600^{\circ} \mathrm{C} .$ Heat is now added until the pressure reaches 1.2 MPa. Find the final temperafure, show the $P-V$ diagram and find the work done during the process.

Sanjeev Kumar

Numerade Educator

03:34

Problem 111

A cylinder having an initial volume of $3 \mathrm{m}^{3}$ con tains $0.1 \mathrm{kg}$ of water at $40^{\circ} \mathrm{C}$. The water is then compressed in an isothermal quasi-equilibrium process until it has a quality of $50 \%$. Calculate the work done by splitting the process into two steps Assume the water vapor is an ideal gas during the fist step of the process.

Sanjeev Kumar

Numerade Educator

06:29

Problem 112

Air at 200 kPa, $30^{\circ} \mathrm{C}$ is contained in a cylinder/piston arrangement with initial volume $0.1 \mathrm{m}^{3} .$ The inside pressure balances ambient pressure of $100 \mathrm{kPa}$ plus an externally imposed force that is proportional to $V^{0.5}$. Now heat is transferred to the system to a final pressure of 225 kPa. Find the final temperature and the work done in the process.

Vipender Yadav

Numerade Educator

04:43

Problem 113

A spring-loaded piston/cylinder arrangement contains $R-134 a$ at $20^{\circ} C, 24 \%$ quality with a volume 50 L. The setup is heated and thus expands, moving the piston. It is noted that when the last drop of liquid disappears the temperature is $40^{\circ} \mathrm{C}$. The heating is stopped when $T=130^{\circ} \mathrm{C}$. Verify that the final pressure is about $1200 \mathrm{kPa}$ by iteration and find the work done in the process.

Sanjeev Kumar

Numerade Educator

01:55

Problem 114

A piston/cylinder setup (Fig. P4.68) contains 1 kg of water at $20^{\circ} \mathrm{C}$ with a volume of $0.1 \mathrm{m}^{3} .$ Initially, the piston rests on some stops with the top surface open to the atmosphere, $P_{0},$ and a mass such that a water pressure of $400 \mathrm{kPa}$ will lift it. To what temperature should the water be heated to lift the piston? If it is heated to saturated yapor, find the final temperature, volume, and work,

Sanjeev Kumar

Numerade Educator

18:01

Problem 115

Two springs with the same spring constant are installed in a massless piston/cylinder arrangement with the outside air at $100 \mathrm{kPa}$. If the piston is at the bottom, both springs are relaxed, and the second spring comes in contact with the piston at $V=2 \mathrm{m}^{3} .$ The cylinder (Fig. P4.11 5 ) contains ammonia initially at $-2^{\circ} \mathrm{C}, x=0.13$ $V=1 \mathrm{m}^{3},$ which is then heated until the pressure finally reaches $1200 \mathrm{kPa}$. At what pressure will the piston touch the second spring? Find the final temperature and the total work done by the ammonia.

Mohammad Mehran

Numerade Educator

02:47

Problem 116

Find the work in the process described in Problem 3.101

Sanjeev Kumar

Numerade Educator

00:51

Problem 117

The electric company charges the customers per kilowatt-hour. What is that in English units?

Sanjeev Kumar

Numerade Educator

00:46

Problem 118

Work as $F \Delta x$ has units of lbf/ft. What is that in Btu?

Sanjeev Kumar

Numerade Educator

01:23

Problem 119

Work of 2.5 Btu must be delivered on a rod from a pneumatic piston/cylinder where the air pressure is limited to 75 psia. What diameter cylinder should I have to restrict the rod motion to maximum 2 ft?

Sanjeev Kumar

Numerade Educator

02:27

Problem 120

A force of 300 lbf moves a truck at $40 \mathrm{mi} / \mathrm{h}$ up a hill. What is the power?

Shahab Ullah

Numerade Educator

02:06

Problem 121

A 1200 -hp dragster engine drives a car with a speed of $65 \mathrm{mi} / \mathrm{h}$. How much force is between the tires and the road?

Shahab Ullah

Numerade Educator

01:23

Problem 122

A 1200 -hp dragster engine has a drive shaft rotating at 2000 RPM. How much torque is on the shaft?

Shahab Ullah

Numerade Educator

05:19

Problem 123

A bulldozer pushes 1000 lbm of dirt 300 ft with a force of 400 lbf. It then lifts the dirt 10 ft up to put it in a dump truck. How much work did it do in each situation?

Shahab Ullah

Numerade Educator

01:57

Problem 124

A steam radiator in a room at 75 F has saturated water vapor at 16 lbf/in $^{2}$ flowing through it when the inlet and exit valves are closed. What is the pressure and the quality of the water when it has cooled to 75 F? How much work is done?

Sanjeev Kumar

Numerade Educator

03:10

Problem 125

A linear spring, $F=k_{s}\left(x-x_{0}\right),$ with spring constant $k_{s}=35$ lbf/ft, is stretched until it is 2.5 in. longer. Find the required force and work input.

Shahab Ullah

Numerade Educator

02:04

Problem 126

Two hydraulic cylinders maintain a pressure of 175 psia. One has a cross-sectional area of $0.1 \mathrm{ft}^{2},$ the other one of $0.3 \mathrm{ft}^{2} .$ To deliver $1 \mathrm{Btu}$ of work to the piston, how large a displacement $(V)$ and piston motion $H$ are needed for each cylinder? Neglect $P_{\text {atm }}$

Mohammad Mehran

Numerade Educator

01:30

Problem 127

A piston/cylinder has $15 \mathrm{ft}$ of liquid $70 \mathrm{F}$ water on top of the piston $(m=0)$ with cross-sectional area of $1 \mathrm{ft}^{2}$ (see Fig. $\mathrm{P} 2.57$ ). Air is let in under the piston, which rises and pushes the water out over the top edge. Find the necessary work to 4 push all the water out, and plot the process in a $P-V$ diagram.

Sanjeev Kumar

Numerade Educator

05:39

Problem 128

A cylinder fitted with a frictionless piston contains 10 lbm of superheated refrigerant $R-134 a$ vapor at $100 \mathrm{lbf} / \mathrm{in}^{2}, 300 \mathrm{F}$. The setup is cooled at constant pressure until the $R-134$ a reaches a quality of $25 \% .$ Calculate the work done in the process.

Mohammad Mehran

Numerade Educator

02:26

Problem 129

The gas space above the water in a closed storage tank contains nitrogen at $80 \mathrm{F}, 15 \mathrm{lbf} / \mathrm{in}^{2}$ Total tank volume is $150 \mathrm{ft}^{3}$, and there is 1000 Ibm of water at $80 \mathrm{F}$. An additional $1000 \mathrm{lbm}$ of water is now forced into the tank. Assuming constant temperature throughout, find the final pressure of the nitrogen and the work done on the nitrogen in this process

Sanjeev Kumar

Numerade Educator

06:05

Problem 130

A cylinder having an initial volume of $100 \mathrm{ft}^{3}$ contains 0.2 lbm of water at 100 F. The water is then compressed in an isothermal quasiequilibrium process until it has a quality of $50 \%$. Calculate the work done in the process assuming water vapor is an ideal gas.

Mohammad Mehran

Numerade Educator

02:25

Problem 131

Helium gas expands from 20 psia, 600 R, and 9 $\mathrm{ft}^{3}$ to 15 psia in a polytropic process with $n=$ 1.667. How much work does it give out?

Narayan Hari

Numerade Educator

00:58

Problem 132

Consider a mass going through a polytropic process where pressure is directly proportional to volume $(n=-1) .$ The process starts with $P=0, V=0$ and ends with $P=90 \mathrm{lbf} / \mathrm{in}^{2}$
$V=0.4 \mathrm{ft}^{3} .$ The physical setup could be as in Problem $2.83 .$ Find the boundary work done by the mass.

Narayan Hari

Numerade Educator

01:12

Problem 133

The piston/cylinder shown in Fig. P4.48 contains carbon dioxide at $50 \mathrm{lbf} / \mathrm{in}^{2}, 200 \mathrm{F}$ with a volume of $5 \mathrm{ft}^{3}$. Mass is added at such a rate that the gas compresses according to the relation $P Y^{1.2}=$ constant to a final temperature of $350 \mathrm{F}$. Determine the work done during the process.

Narayan Hari

Numerade Educator

02:06

Problem 134

Find the specific work for Problem $3.156 \mathrm{E}$

Sanjeev Kumar

Numerade Educator

01:46

Problem 135

Consider a two-part process with an expansion from 3 to $6 \mathrm{ft}^{3}$ at a constant pressure of 20 16f/in $^{2}$ followed by an expansion from 6 to $12 \mathrm{ft}^{3}$ with a linearly rising pressure from $20 \mathrm{lbf} / \mathrm{in}^{2}$ ending at 40 lbf/in'. Show the process in a $P-V$ diagram and find the boundary work.

Narayan Hari

Numerade Educator

11:42

Problem 136

A piston/cylinder has 2 lbm of $R-134 a$ at state with $200 \mathrm{F}, 90 \mathrm{lbf} / \mathrm{in}^{2},$ and is then brought to saturated vapor, state $2,$ by cooling while the piston is locked with a pin. Now the piston is balanced with an additional constant force and the pin is removed. The cooling continues to state $3,$ where the $R-134 a$ is saturated liquid. Show the processes in a $P-V$ diagram and find the work in each of the two steps, 1 to 2 and 2 to 3

Mohammad Mehran

Numerade Educator

03:07

Problem 137

A cylinder containing 2 lbm of ammonia has an externally loaded piston. Initially the ammonia is at $280 \mathrm{lbf} / \mathrm{in}^{2}, 360 \mathrm{F}$. It is now cooled to saturated vapor at $105 \mathrm{F}$, and then further cooled to $65 \mathrm{F}$, at which point the quality is $50 \%$. Find the total work for the process, assuming a piecewise linear variation of $P$ versus $V$

Sanjeev Kumar

Numerade Educator

01:04

Problem 138

A 1 -ft-long steel rod with a 0.5 -in. diameter is stretched in a tensile test. What is the required work to obtain a relative strain of $0.1 \% ?$ The modulus of elasticity of steel is $30 \times 10^{6}$ lbf/in $^{2}$

Narayan Hari

Numerade Educator

03:40

Problem 139

An escalator raises a 200 -lbm bucket of sand 30 $\mathrm{ft}$ in 1 min. Determine the total amount of work done and the instantaneous rate of work during the process.

Shahab Ullah

Numerade Educator

01:02

Problem 140

A piston/cylinder of diameter 10 in. moves a piston with a velocity of $18 \mathrm{ft} / \mathrm{s}$. The instantaneous pressure if 100 psia. What is the volume displacement rate, the force and the transmitted power?

Sanjeev Kumar

Numerade Educator

03:09

Problem 141

The sun shines on a $1500-\mathrm{ft}^{2}$ road surface so it is at 115 F. Below the 2 -in. -thick asphalt, average conductivity of 0.035 Btu/h $\mathrm{A} \mathrm{F}$, is a layer of compacted rubble at a temperature of 60 F. Find the rate of heat transfer to the rubble.

Shahab Ullah

Numerade Educator

02:57

Problem 142

A water heater is covered up with insulation boards over a total surface area of $30 \mathrm{ft}^{2}$. The inside board surface is at $175 \mathrm{F}$, the outside surface is at $70 \mathrm{F}$, and the board material has a conductivity of 0.05 Btu/h ft $\mathrm{F.}$ How thick should the board be to limit the heat transfer loss to $720 \mathrm{Btu} / \mathrm{h} ?$

Shahab Ullah

Numerade Educator

01:11

Problem 143

The black grille on the back of a refrigerator has a surface temperature of $95 \mathrm{F}$ with a total surface area of $10 \mathrm{ft}^{2}$. Heat transfer to the room air at $70 \mathrm{F}$ takes place with an average convective heat transfer coefficient of 3 Btu/h $\mathrm{ft}^{2}$ R. How much energy can be removed during 15 min of operation?

Narayan Hari

Numerade Educator

03:33

Problem 144

In Problem 4.48 , determine the work done by the carbon dioxide at any point during the process.

Sanjeev Kumar

Numerade Educator

02:47

Problem 145

In Problem 4.112 , determine the work done by the air at any point during the process

Sanjeev Kumar

Numerade Educator

07:16

Problem 146

A piston/cylinder arrangement of initial volume $0.025 \mathrm{m}^{3}$ contains saturated water vapor at $200^{\circ} \mathrm{C}$ The steam now expands in a quasi-equilibrium isothermal process to a final pressure of $200 \mathrm{kPa}$ while it does work against the piston. Determine the work done in this process by a numerical integration (summation) of the area below the $P-V$ process curve. Compute about 10 points along the curve by using the computerized software to get the volume at $200^{\circ} \mathrm{C}$ and the various pressures. How different is the work calculated if ideal gas is assumed?

Keshav Singh

Numerade Educator

04:26

Problem 147

Reconsider the process in Problem 4.60 in which three states were specified. Solve the problem by fitting a single smooth curve ( $P$ versus $v$ ) through the three points. Map out the path followed (including temperature and quality) during the process.

Mohammad Mehran

Numerade Educator

01:24

Problem 148

Write a computer program to determine the boundary movement work for a specified substance undergoing a process for a given set of data (values of pressure and corresponding volume during the process.

Prem Bijarniya

Numerade Educator

04:07

Problem 149

Ammonia vapor is compressed inside a cylinder by an external force acting on the piston. The ammonia is initially at $30^{\circ} \mathrm{C}, 500 \mathrm{kPa}$, and the final pressure is $1400 \mathrm{kPa}$. The following data have been measured for the process: $$\begin{array}{clllllll}
\hline \text { Pressure, } & 500 & 653 & 802 & 945 & 1100 & 1248 & 1400 \\
\mathrm{kPa} & & & & & & \\
\text { Volume, L } & 1.25 & 1.08 & 0.96 & 0.84 & 0.72 & 0.60 & 0.50 \\
\hline
\end{array}$$ Determine the work done by the ammonia by summing the area below the $P-V$ process curve. As you plot it, $P$ is the height and the change in volume is the base of a number of rectangles.

Saikat Chatterjee

Numerade Educator

02:58

Problem 150

A substance is brought from a state of $P_{1}, v_{1}$ to a state of $P_{2}, v_{2}$ in a piston/cylinder arrangement. Assume that the process can be approximated as a polytropic process. Write a program that will find the polytropic exponent, $n,$ and the boundary work per unit mass. The four state properties are input variables. Check the program with cases that you can easily hand calculate.

Guilherme Barros

Numerade Educator

00:44

Problem 151

Assume that you have a plate of $A=1 \mathrm{m}^{2}$ with thickness $L=0.02 \mathrm{m}$ over which there is a temperature difference of $20^{\circ} \mathrm{C}$. Find the conductivity, $\mathrm{k}$, from the literature and compare the heat transfer rates if the plate substance is a metal like aluminum or steel, or wood, foam insulation, air, argon, or liquid water. Assume the average substance temperature is $25^{\circ} \mathrm{C}$

Sanjeev Kumar

Numerade Educator

01:35

Problem 152

Make a list of household appliances such as refrigerators, electric heaters, vacuum cleaners, hair dryers, TVs, stereo sets, and any others you may think of. For each, list its energy consumption and explain where you have energy transfer as work and where there is heat transfer.

Sanjeev Kumar

Numerade Educator