College Physics With an Integrated Approach to Forces and Kinematics

Alan Giambattista, Betty McCarthy Richardson , Robert C. Richardson

Chapter 15

Thermodynamics - all with Video Answers

Educators

Chapter Questions

Problem 1

On a cold day, Ming rubs her hands together to warm them up. She presses her hands together with a force of $5.0 \mathrm{~N}$. Each time she rubs them back and forth they move a distance of $16 \mathrm{~cm}$ with a coefficient of kinetic friction of $0.45 .$ Assuming no heat flow to the surroundings, after she has rubbed her hands back and forth eight times, by how much has the internal energy of her hands increased?

Ythan Reyes

Ythan Reyes

Numerade Educator

Problem 2

A system takes in $550 \mathrm{~J}$ of heat while performing $840 \mathrm{~J}$ of work. What is the change in internal energy of the system?

David Kobylarz

Numerade Educator

Problem 3

The internal energy of a system increases by $400 \mathrm{~J}$ while $500 \mathrm{~J}$ of work are performed on it. What was the heat flow into or out of the system?

Ythan Reyes

Numerade Educator

Problem 4

A model steam engine of $1.00-\mathrm{kg}$ mass pulls eight cars of $1.00-\mathrm{kg}$ mass each. The cars start at rest and reach a velocity of $3.00 \mathrm{~m} / \mathrm{s}$ in a time of $3.00 \mathrm{~s}$ while moving a distance of $4.50 \mathrm{~m}$. During that time, the engine takes in $135 \mathrm{~J}$ of heat. What is the change in the internal energy of the engine?

David Kobylarz

Numerade Educator

Problem 5

A monatomic ideal gas at $27^{\circ} \mathrm{C}$ undergoes a constant pressure process from $A$ to $B$ and a constant volume process from $B$ to $C$. Find the total work done during these two processes.

Ythan Reyes

Numerade Educator

Problem 6

A monatomic ideal gas at $27^{\circ} \mathrm{C}$ undergoes a constant volume process from $A$ to $B$ and a constant pressure process from $B$ to $C$. Find the total work done during these two processes.

David Kobylarz

Numerade Educator

Problem 7

An ideal monatomic gas is taken through the cycle in the $P V$ diagram. (a) If there are $0.0200 \mathrm{~mol}$ of this gas,
what are the temperature and pressure at point $C ?(\mathrm{~b})$ What is the change in internal energy of the gas as it is taken from $A$ to $B ?(\mathrm{c})$ How much work is done by this gas per cycle? (d) What is the total change in internal energy of this gas in one cycle?

Ythan Reyes

Numerade Educator

Problem 8

An ideal gas is in contact with a heat reservoir so that it remains at a constant temperature of $300.0 \mathrm{~K}$. The gas is compressed from a volume of $24.0 \mathrm{~L}$ to a volume of $14.0 \mathrm{~L}$. During the process, the mechanical device pushing the piston to compress the gas is found to expend $5.00 \mathrm{~kJ}$ of energy. How much heat flows between the heat reservoir and the gas and in what direction does the heat flow occur?

David Kobylarz

Numerade Educator

Problem 9

Suppose $1.00 \mathrm{~mol}$ of oxygen is heated at constant pressure of $1.00$ atm from $10.0^{\circ} \mathrm{C}$ to $25.0^{\circ} \mathrm{C}$. (a) How much heat is absorbed by the gas? (b) Using the ideal gas law, calculate the change of volume of the gas in this process. (c) What is the work done by the gas during this expansion? (d) From the first law, calculate the change of internal energy of the gas in this process.

Ythan Reyes

Numerade Educator

Problem 10

Suppose a monatomic ideal gas is changed from state $A$ to state $D$ by one of the processes shown on the $P V$ diagram. (a) Find the total work done on the gas if it follows the constant vol-
ume path $A-B$ followed by the constant pressure path $B-C-D .$ (b) Calculate the total change in internal energy of the gas during the entire process and the total heat flow into the gas.

Brandy Heflin

Numerade Educator

Problem 11

Repeat Problem 10 for the case when the gas follows the constant temperature path $A-C$ followed by the constant pressure path $C-D$.

Matthew Muscat

Numerade Educator

Problem 12

Repeat Problem 10 for the case when the gas follows the constant pressure path $A-E$ followed by the constant temperature path $E-D$.

David Kobylarz

Numerade Educator

Problem 13

A heat engine follows the cycle shown in the figure. (a) How much net work is
done by the engine in one cycle? (b) What is the heat flow into the engine per cycle?

Ythan Reyes

Numerade Educator

Problem 14

What is the efficiency of an electric generator that produces $1.17 \mathrm{~kW} \cdot \mathrm{h}$ per $\mathrm{kg}$ of coal burned? The heat of combustion of coal is $6.71 \times 10^{6} \mathrm{~J} / \mathrm{kg}$.

David Kobylarz

Numerade Educator

Problem 15

A heat pump delivers heat at a rate of $7.81 \mathrm{~kW}$ for $10.0 \mathrm{~h}$. If its coefficient of performance is $6.85$, how much heat is taken from the cold reservoir during that time?

Ythan Reyes

Numerade Educator

Problem 16

(a) How much heat does an engine with an efficiency of $33.3 \%$ absorb in order to deliver $1.00 \mathrm{~kJ}$ of work?
(b) How much heat is exhausted by the engine?

David Kobylarz

Numerade Educator

Problem 17

The efficiency of an engine is $0.21$. For every $1.00 \mathrm{~kJ}$ of heat absorbed by the engine, how much (a) net work is done by it and (b) heat is released by it?

Ythan Reyes

Numerade Educator

Problem 18

A certain engine can propel a $1800-\mathrm{kg}$ car from rest to a speed of $27 \mathrm{~m} / \mathrm{s}$ in $9.5 \mathrm{~s}$ with an efficiency of $27 \%$. What are the rate of heat flow into the engine at the high temperature and the rate of heat flow out of the engine at the low temperature?

David Kobylarz

Numerade Educator

Problem 19

The United States generates about $5.0 \times 10^{16} \mathrm{~J}$ of electric energy a day. This energy is equivalent to work, since it can be converted into work with almost $100 \%$ efficiency by an electric motor. (a) If this energy is generated by power plants with an average efficiency of $0.30$, how much heat is dumped into the environment each day? (b) How much water would be required to absorb this heat if the water temperature is not to increase more than $2.0^{\circ} \mathrm{C}$ ?

Matthew Muscat

Numerade Educator

Problem 20

The intensity (power per unit area) of the sunlight incident on Earth's surface, averaged over a $24-h$ period, is about $0.20 \mathrm{~kW} / \mathrm{m}^{2}$. If a solar power plant is to be built with an output capacity of $1.0 \times 10^{9} \mathrm{~W}$, how big must the area of the solar energy collectors be for photocells operating at $20.0 \%$ efficiency?

Matthew Muscat

Numerade Educator

Problem 21

An engine releases $0.450 \mathrm{~kJ}$ of heat for every $0.100 \mathrm{~kJ}$ of work it does. What is the efficiency of the engine?

Ythan Reyes

Numerade Educator

Problem 22

An engine works at $30.0 \%$ efficiency. The engine raises a $5.00-\mathrm{kg}$ crate from rest to a vertical height of $10.0 \mathrm{~m}$, at which point the crate has a speed of $4.00 \mathrm{~m} / \mathrm{s}$. How much heat input is required for this engine?

Matthew Muscat

Numerade Educator

Problem 23

How much heat does a heat pump with a coefficient of performance of $3.0$ deliver when supplied with $1.00 \mathrm{~kJ}$ of electricity?

Matthew Muscat

Numerade Educator

Problem 24

An air conditioner whose coefficient of performance is $2.00$ removes $1.73 \times 10^{8} \mathrm{~J}$ of heat from a room per day.
How much does it cost to run the air conditioning unit per day if electricity costs $\$ 0.10$ per kilowatt-hour? (Note that 1 kilowatt-hour $=3.6 \times 10^{6} \mathrm{~J}$.)

Matthew Muscat

Numerade Educator

Problem 25

An ideal engine has an efficiency of $0.725$ and uses gas from a hot reservoir at a temperature of $622 \mathrm{~K}$. What is the temperature of the cold reservoir to which it exhausts heat?

Matthew Muscat

Numerade Educator

Problem 26

A heat engine takes in $125 \mathrm{~kJ}$ of heat from a reservoir at $815 \mathrm{~K}$ and exhausts $82 \mathrm{~kJ}$ to a reservoir at $293 \mathrm{~K}$.
(a) What is the efficiency of the engine? (b) What is the efficiency of an ideal engine operating between the same two reservoirs?

Matthew Muscat

Numerade Educator

Problem 27

In a certain steam engine, the boiler temperature is $127^{\circ} \mathrm{C}$ and the cold reservoir temperature is $27^{\circ} \mathrm{C}$. While this engine does $8.34 \mathrm{~kJ}$ of work, what minimum amount of heat must be discharged into the cold reservoir?

Matthew Muscat

Numerade Educator

Problem 28

Calculate the maximum possible efficiency of a heat engine that uses surface lake water at $18.0^{\circ} \mathrm{C}$ as a source
of heat and rejects waste heat to the water $0.100 \mathrm{~km}$ below the surface where the temperature is $4.0^{\circ} \mathrm{C}$.

Matthew Muscat

Numerade Educator

Problem 29

An ideal refrigerator removes heat at a rate of $0.10 \mathrm{~kW}$ from its interior $\left(+2.0^{\circ} \mathrm{C}\right)$ and exhausts heat at $40.0^{\circ} \mathrm{C}$. How much electrical power is used?

Matthew Muscat

Numerade Educator

Problem 30

A heat pump is used to heat a house with an interior temperature of $20.0^{\circ} \mathrm{C}$. On a chilly day with an outdoor temperature of $-10.0^{\circ} \mathrm{C}$, what is the minimum work that the pump requires in order to deliver $1.0 \mathrm{~kJ}$ of heat to the house? ( Wy tutorial: heat pump)

Matthew Muscat

Numerade Educator

Problem 31

A coal-fired electrical generating station can use a higher $T_{\mathrm{H}}$ than a nuclear plant; for safety reasons the core of a nuclear reactor is not allowed to get as hot as coal. Suppose that $T_{\mathrm{H}}=727^{\circ} \mathrm{C}$ for a coal station but $T_{\mathrm{H}}=527^{\circ} \mathrm{C}$ for a nuclear station. Both power plants exhaust waste heat into a lake at $T_{\mathrm{C}}=27^{\circ} \mathrm{C}$. How much waste heat does each plant exhaust into the lake to produce $1.00 \mathrm{MJ}$ of electricity? Assume both operate as reversible engines. ( Worial: power stations)

Matthew Muscat

Numerade Educator

Problem 32

Two engines operate between the same two temperatures of $750 \mathrm{~K}$ and $350 \mathrm{~K}$, and have the same rate of heat input. One of the engines is a reversible engine with a power output of $2.3 \times 10^{4} \mathrm{~W}$. The second engine has an efficiency of $42 \%$. What is the power output of the second engine?

Matthew Muscat

Numerade Educator

Problem 33

(a) Calculate the efficiency of a reversible engine that operates between the temperatures $600.0^{\circ} \mathrm{C}$ and $300.0^{\circ} \mathrm{C}$. (b) If the engine absorbs $420.0 \mathrm{~kJ}$ of heat from the hot reservoir, how much does it exhaust to the cold reservoir?

Matthew Muscat

Numerade Educator

Problem 34

A reversible engine with an efficiency of $30.0 \%$ has $T_{\mathrm{C}}=310.0 \mathrm{~K}$. (a) What is $T_{\mathrm{H}}$ ? (b) How much heat is exhausted for every $0.100 \mathrm{~kJ}$ of work done?

Matthew Muscat

Numerade Educator

Problem 35

An electric power station generates steam at $500.0^{\circ} \mathrm{C}$ and condenses it with river water at $27^{\circ} \mathrm{C}$. By how much would its theoretical maximum efficiency decrease if it had to switch to cooling towers that condense the steam at $47^{\circ} \mathrm{C}$ ?

Matthew Muscat

Numerade Educator

Problem 36

An oil-burning electric power plant uses steam at $773 \mathrm{~K}$ to drive a turbine, after which the steam is expelled at $373 \mathrm{~K}$. The engine has an efficiency of $0.40$. What is the theoretical maximum efficiency possible at those temperatures?

Matthew Muscat

Numerade Educator

Problem 37

An inventor proposes a heat engine to propel a ship, using the temperature difference between the water at the surface and the water $10 \mathrm{~m}$ below the surface as the two reservoirs. If these temperatures are $15.0^{\circ} \mathrm{C}$ and $10.0^{\circ} \mathrm{C}$, respectively, what is the maximum possible efficiency of the engine?

Matthew Muscat

Numerade Educator

Problem 38

A heat engine uses the warm air at the ground as the hot reservoir and the cooler air at an altitude of several thousand meters as the cold reservoir. If the warm air is at $37^{\circ} \mathrm{C}$ and the cold air is at $25^{\circ} \mathrm{C}$, what is the maximum possible efficiency for the engine?

Matthew Muscat

Numerade Educator

Problem 39

A reversible refrigerator has a coefficient of performance of $3.0 .$ How much work must be done to freeze 1.0 kg of liquid water initially at $0{ }^{\circ} \mathrm{C}$ ?

Matthew Muscat

Numerade Educator

Problem 40

An engine operates between temperatures of $650 \mathrm{~K}$ and $350 \mathrm{~K}$ at $65.0 \%$ of its maximum possible efficiency.
(a) What is the efficiency of this engine? (b) If $6.3 \times 10^{3} \mathrm{~J}$ is exhausted to the low temperature reservoir, how much work does the engine do?

Matthew Muscat

Numerade Educator

Problem 41

A town is planning on using the water flowing through a river at a rate of $5.0 \times 10^{6} \mathrm{~kg} / \mathrm{s}$ to carry away the heat from a new power plant. Environmental studies indicate that the temperature of the river should only increase by $0.50^{\circ} \mathrm{C}$. The maximum design efficiency for this plant is $30.0 \%$. What is the maximum possible power this plant can produce?

Matthew Muscat

Numerade Educator

Problem 42

Show that the coefficient of performance for a reversible heat pump is $1 /\left(1-T_{\mathrm{C}} / T_{\mathrm{H}}\right)$.

Matthew Muscat

Numerade Educator

Problem 43

On a hot day, you are in a sealed, insulated room. The room contains a refrigerator, operated by an electric motor. The motor does work at the rate of $250 \mathrm{~W}$ when it is running. Assume the motor is ideal (no friction or electrical resistance) and that the refrigerator operates on a reversible cycle. In an effort to cool the room, you turn on the refrigerator and open its door. Let the temperature in the room be $320 \mathrm{~K}$ when this process starts, and the temperature in the cold compartment of the refrigerator be $256 \mathrm{~K}$. At what net rate is heat added to $(+)$ or subtracted from $(-)$ the room and all of its contents?

Matthew Muscat

Numerade Educator

Problem 44

Show that the coefficient of performance for a reversible refrigerator is $1 /\left[\left(T_{\mathrm{H}} / T_{\mathrm{C}}\right)-1\right]$.

Matthew Muscat

Numerade Educator

Problem 45

Show that in a reversible engine the amount of heat $Q_{C}$ exhausted to the cold reservoir is related to the net work done $W_{\text {net }}$ by
$$
Q_{\mathrm{C}}=\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}-T_{\mathrm{C}}} W_{\mathrm{net}}
$$

Matthew Muscat

Numerade Educator

Problem 46

List these in order of increasing entropy: (a) $0.01 \mathrm{~mol}$ of $\mathrm{N}_{2}$ gas in a 1-L container at $0{ }^{\circ} \mathrm{C}$; (b) $0.01 \mathrm{~mol}$ of $\mathrm{N}_{2}$ gas in a 2-L container at $0{ }^{\circ} \mathrm{C}$; (c) $0.01 \mathrm{~mol}$ of liquid $\mathrm{N}_{2}$.

Matthew Muscat

Numerade Educator

Problem 47

List these in order of increasing entropy: (a) $0.5 \mathrm{~kg}$ of ice and $0.5 \mathrm{~kg}$ of (liquid) water at $0^{\circ} \mathrm{C} ;$ (b) $1 \mathrm{~kg}$ of ice at $0^{\circ} \mathrm{C} ;$ (c) $1 \mathrm{~kg}$ of (liquid) water at $0{ }^{\circ} \mathrm{C} ;$ (d) $1 \mathrm{~kg}$ of water at $20^{\circ} \mathrm{C}$.

Matthew Muscat

Numerade Educator

Problem 48

An ice cube at $0.0^{\circ} \mathrm{C}$ is slowly melting. What is the change in the ice cube's entropy for each $1.00 \mathrm{~g}$ of ice that melts?

Matthew Muscat

Numerade Educator

Problem 49

From Table $14.4$, we know that approximately $2256 \mathrm{~kJ}$ are needed to transform $1.00 \mathrm{~kg}$ of water at $100^{\circ} \mathrm{C}$ to steam at $100^{\circ} \mathrm{C}$. What is the change in entropy of $1.00 \mathrm{~kg}$ of water evaporating at $100.0^{\circ} \mathrm{C} ?$ (Specify whether the change in entropy is an increase, $+$, or a decrease, $-.$.)

Matthew Muscat

Numerade Educator

Problem 50

What is the change in entropy of $10 \mathrm{~g}$ of steam at $100^{\circ} \mathrm{C}$ as it condenses to water at $100^{\circ} \mathrm{C}$ ? By how much does the entropy of the universe increase in this process?

Matthew Muscat

Numerade Educator

Problem 51

A large block of copper initially at $20.0^{\circ} \mathrm{C}$ is placed in a vat of hot water $\left(80.0^{\circ} \mathrm{C}\right)$. For the first $1.0 \mathrm{~J}$ of heat that flows from the water into the block, find (a) the entropy change of the block, (b) the entropy change of the water, and (c) the entropy change of the universe. Note that the temperatures of the block and water are essentially unchanged by the flow of only $1.0 \mathrm{~J}$ of heat.

Matthew Muscat

Numerade Educator

Problem 52

A large, cold $\left(0.0^{\circ} \mathrm{C}\right)$ block of iron is immersed in a tub of hot $\left(100.0^{\circ} \mathrm{C}\right)$ water. In the first $10.0 \mathrm{~s}, 41.86 \mathrm{~kJ}$ of heat are transferred, although the temperatures of the water and the iron do not change much in this time. Ignoring heat flow between the system (iron + water) and its surroundings, calculate the change in entropy of the system (iron + water) during this time.

Matthew Muscat

Numerade Educator

Problem 53

On a cold winter day, the outside temperature is $-15.0^{\circ} \mathrm{C}$. Inside the house the temperature is $+20.0^{\circ} \mathrm{C}$. Heat flows out of the house through a window at a rate of $220.0 \mathrm{~W}$. At what rate is the entropy of the universe changing due to this heat conduction through the window?

Matthew Muscat

Numerade Educator

Problem 54

Within an insulated system, $418.6 \mathrm{~kJ}$ of heat is conducted through a copper rod from a hot reservoir at $+200.0^{\circ} \mathrm{C}$ to a cold reservoir at $+100.0^{\circ} \mathrm{C}$. (The reservoirs are so big that this heat exchange does not change their temperatures appreciably.) What is the net change in entropy of the system, in $\mathrm{kJ} / \mathrm{K}$ ?

Matthew Muscat

Numerade Educator

Problem 55

A student eats 2000 kcal per day. (a) Assuming that all of the food energy is released as heat, what is the rate of heat released (in watts)? (b) What is the rate of change of entropy of the surroundings if all of the heat is released into air at room temperature $\left(20^{\circ} \mathrm{C}\right) ?$

Matthew Muscat

Numerade Educator

Problem 56

The motor that drives a reversible refrigerator produces $148 \mathrm{~W}$ of useful power. The hot and cold temperatures of the heat reservoirs are $20.0^{\circ} \mathrm{C}$ and $-5.0^{\circ} \mathrm{C}$. What is the maximum amount of ice it can produce in $2.0 \mathrm{~h}$ from water that is initially at $8.0^{\circ} \mathrm{C}$ ?

Matthew Muscat

Numerade Educator

Problem 57

An engineer designs a ship that gets its power in the following way: The engine draws in warm water from the ocean, and after extracting some of the water's internal energy, returns the water to the ocean at a temperature $14.5^{\circ} \mathrm{C}$ lower than the ocean temperature. If the ocean is at a uniform temperature of $17^{\circ} \mathrm{C}$, is this an efficient engine? Will the engineer's design work?

Shahab Ullah

Numerade Educator

Problem 58

A balloon contains $200.0 \mathrm{~L}$ of nitrogen gas at $20.0^{\circ} \mathrm{C}$ and at atmospheric pressure. How much energy must be added to raise the temperature of the nitrogen to $40.0^{\circ} \mathrm{C}$ while allowing the balloon to expand at atmospheric pressure?

Matthew Muscat

Numerade Educator

Problem 59

An ideal gas is heated at a constant pressure of $2.0 \times 10^{5}$ Pa from a temperature of $-73^{\circ} \mathrm{C}$ to a temperature of $+27^{\circ} \mathrm{C}$. The initial volume of the gas is $0.10 \mathrm{~m}^{3}$. The heat energy supplied to the gas in this process is $25 \mathrm{~kJ}$. What is the increase in internal energy of the gas?

Matthew Muscat

Numerade Educator

Problem 60

If the pressure on a fish increases from $1.1$ to $1.2 \mathrm{~atm}$, its swim bladder decreases in volume from $8.16 \mathrm{~mL}$ to
$7.48 \mathrm{~mL}$ while the temperature of the air inside remains constant. How much work is done on the air in the bladder?

Matthew Muscat

Numerade Educator

Problem 61

A monatomic ideal gas follows the cyclic process shown in the figure. The temperature of the point at the bottom left of the triangle is $470.0 \mathrm{~K}$.
(a) How much net work does this engine do per cycle? (b) What is the maximum temperature of this engine? (c) How many moles of gas are used in this engine?

Matthew Muscat

Numerade Educator

Problem 62

For a reversible engine, will you obtain a better efficiency by increasing the high-temperature reservoir by an amount $\Delta T$ or decreasing the low-temperature reservoir by the same amount $\Delta T$ ?

Matthew Muscat

Numerade Educator

Problem 63

A $0.50-\mathrm{kg}$ block of iron $[c=0.44 \mathrm{~kJ} /(\mathrm{kg} \cdot \mathrm{K})]$ at $20.0^{\circ} \mathrm{C}$
is in contact with a $0.50-\mathrm{kg}$ block of aluminum $[c=$ $0.900 \mathrm{~kJ} /(\mathrm{kg} \cdot \mathrm{K})]$ at a temperature of $20.0{ }^{\circ} \mathrm{C}$. The sys-
tem is completely isolated from the rest of the universe. Suppose heat flows from the iron into the aluminum until the temperature of the aluminum is $22.0^{\circ} \mathrm{C}$.
(a) From the first law, calculate the final temperature of the iron. (b) Estimate the entropy change of the system.
(c) Explain how the result of part (b) shows that this process is impossible. [Hint: Since the system is isolated, $\left.\Delta S_{\text {System }}=\Delta S_{\text {Universe }} .\right]$

Matthew Muscat

Numerade Educator

Problem 64

List these in order of increasing entropy: (a) $1 \mathrm{~mol}$ of water at $20^{\circ} \mathrm{C}$ and $1 \mathrm{~mol}$ of ethanol at $20^{\circ} \mathrm{C}$ in separate containers; (b) a mixture of 1 mol of water at $20^{\circ} \mathrm{C}$ and $1 \mathrm{~mol}$ of ethanol at $20^{\circ} \mathrm{C} ;$ (c) $0.5 \mathrm{~mol}$ of water at $20^{\circ} \mathrm{C}$
and $0.5 \mathrm{~mol}$ of ethanol at $20^{\circ} \mathrm{C}$ in separate containers;(d) a mixture of $1 \mathrm{~mol}$ of water at $30^{\circ} \mathrm{C}$ and $1 \mathrm{~mol}$ of ethanol at $30^{\circ} \mathrm{C}$.

Matthew Muscat

Numerade Educator

Problem 65

Suppose you mix $4.0 \mathrm{~mol}$ of a monatomic gas at $20.0^{\circ} \mathrm{C}$ and $3.0 \mathrm{~mol}$ of another monatomic gas at $30.0^{\circ} \mathrm{C}$. If the mixture is allowed to reach equilibrium, what is the final temperature of the mixture? [Hint: Use energy conservation.]

Matthew Muscat

Numerade Educator

Problem 66

A balloon contains $160 \mathrm{~L}$ of nitrogen gas at $25^{\circ} \mathrm{C}$ and $1.0$ atm. How much energy must be added to raise the temperature of the nitrogen to $45^{\circ} \mathrm{C}$ while allowing the balloon to expand at atmospheric pressure?

Matthew Muscat

Numerade Educator

Problem 67

The efficiency of a muscle during weight lifting is equal to the work done in lifting the weight divided by the total energy output of the muscle (work done plus internal energy dissipated in the muscle). Determine the efficiency of a muscle that lifts a 161-N weight through a vertical displacement of $0.577 \mathrm{~m}$ and dissipates $139 \mathrm{~J}$ in the process.

Matthew Muscat

Numerade Educator

Problem 68

(a) What is the entropy change of $1.00 \mathrm{~mol}$ of $\mathrm{H}_{2} \mathrm{O}$ when it changes from ice to water at $0.0^{\circ} \mathrm{C} ?(\mathrm{~b})$ If the ice is in contact with an environment at a temperature of $10.0^{\circ} \mathrm{C}$, what is the entropy change of the universe when the ice melts?

Matthew Muscat

Numerade Educator

Problem 69

Estimate the entropy change of $850 \mathrm{~g}$ of water when it is heated from $20.0^{\circ} \mathrm{C}$ to $50.0^{\circ} \mathrm{C}$. [Hint: Assume that the heat flows into the water at an average temperature.]

Matthew Muscat

Numerade Educator

Problem 70

For a more realistic estimate of the maximum coefficient of performance of a heat pump, assume that a heat pump takes in heat from outdoors at $10^{\circ} \mathrm{C}$ below the ambient outdoor temperature, to account for the temperature difference across its heat exchanger. Similarly, assume that the output must be $10^{\circ} \mathrm{C}$ hotter than the house (which itself might be kept at $20^{\circ} \mathrm{C}$ ) to make the heat flow into the house. Make a graph of the coefficient of performance of a reversible heat pump under these conditions as a function of outdoor temperature (from $-15^{\circ} \mathrm{C}$ to $+15^{\circ} \mathrm{C}$ in $5^{\circ} \mathrm{C}$ increments $)$

Matthew Muscat

Numerade Educator

Problem 71

A $0.500-\mathrm{kg}$ block of iron at $60.0^{\circ} \mathrm{C}$ is placed in contact with a $0.500$ -kg block of iron at $20.0^{\circ} \mathrm{C}$. (a) The blocks soon come to a common temperature of $40.0^{\circ} \mathrm{C}$. Estimate the entropy change of the universe when this occurs. [Hint: Assume that all the heat flow occurs at an average temperature for each block.] (b) Estimate the entropy change of the universe if, instead, the temperature of the hotter block increased to $80.0^{\circ} \mathrm{C}$ while the temperature of the colder block decreased to $0.0^{\circ} \mathrm{C}$. [Hint: The answer is negative, indicating that the process is impossible.]

Matthew Muscat

Numerade Educator

Problem 72

A container holding $1.20 \mathrm{~kg}$ of water at $20.0^{\circ} \mathrm{C}$ is placed in a freezer that is kept at $-20.0^{\circ} \mathrm{C}$. The water freezes and comes to thermal equilibrium with the interior of the freezer. What is the minimum amount of electrical energy required by the freezer to do this if it operates between reservoirs at temperatures of $20.0^{\circ} \mathrm{C}$ and $-20.0^{\circ} \mathrm{C} ?$

Matthew Muscat

Numerade Educator

Problem 73

A reversible heat engine has an efficiency of $33.3 \%$, removing heat from a hot reservoir and rejecting heat to a cold reservoir at $0^{\circ} \mathrm{C}$. If the engine now operates in reverse, how long would it take to freeze $1.0 \mathrm{~kg}$ of water at $0^{\circ} \mathrm{C}$, if it operates on a power of $186 \mathrm{~W}$ ?

Matthew Muscat

Numerade Educator

Problem 74

Consider a heat engine that is not reversible. The engine uses $1.000 \mathrm{~mol}$ of a diatomic ideal gas. In the first step (A) there is a constant temperature expansion while in contact with a warm reservoir at $373 \mathrm{~K}$ from $P_{1}=1.55 \times 10^{5} \mathrm{~Pa}$ and $V_{1}=2.00 \times 10^{-2} \mathrm{~m}^{3}$ to
$P_{2}=1.24 \times 10^{5} \mathrm{~Pa}$ and $V_{2}=2.50 \times 10^{-2} \mathrm{~m}^{3} .$ Then (B) a
heat reservoir at the cooler temperature of $273 \mathrm{~K}$ is used to cool the gas at constant volume to $273 \mathrm{~K}$ from $P_{2}$ to $P_{3}=0.91 \times 10^{5} \mathrm{~Pa}$. This is followed by (C) a constant temperature compression while still in contact with the cold reservoir at $273 \mathrm{~K}$ from $P_{3}, V_{2}$ to $P_{4}=1.01 \times 10^{5} \mathrm{~Pa}, V_{1}$. The final step (D) is heating the gas at constant volume from $273 \mathrm{~K}$ to $373 \mathrm{~K}$ by being in contact with the warm reservoir again, to return from $P_{4}, V_{1}$ to $P_{1}, V_{1} .$ Find the change in entropy of the cold reservoir in step B. Remember that the gas is always in contact with the cold reservoir. (b) What is the change in entropy of the hot reservoir in step D? (c) Using this information, find the change in entropy of the total system of gas plus reservoirs during the whole cycle.

Matthew Muscat

Numerade Educator

Problem 75

A fish at a pressure of $1.1$ atm has its swim bladder inflated to an initial volume of $8.16 \mathrm{~mL}$. If the fish starts swimming horizontally, its temperature increases from $20.0^{\circ} \mathrm{C}$ to $22.0^{\circ} \mathrm{C}$ as a result of the exertion. (a) Since the fish is still at the same pressure, how much work is done by the air in the swim bladder? [Hint: First find the new volume from the temperature change.] (b) How much heat is gained by the air in the swim bladder? Assume air to be a diatomic ideal gas. (c) If this quantity of heat is lost by the fish, by how much will its temperature decrease? The fish has a mass of $5.00 \mathrm{~g}$ and its specific heat is about $3.5 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)$.

Matthew Muscat

Numerade Educator

Problem 76

Consider the heat engine described in Problem 74 .
(a) For each step in the cycle, find the work done by the gas, the heat flow into or out of the gas, and the change in internal energy of the gas. (b) Find the efficiency of this engine. (c) Compare to the efficiency of a reversible engine that uses the same two reservoirs.

Matthew Muscat

Numerade Educator

Problem 77

A town is considering using its lake as a source of power. The average temperature difference from the top to the bottom is $15^{\circ} \mathrm{C}$, and the average surface temperature is $22^{\circ} \mathrm{C}$. (a) Assuming that the town can set up a reversible engine using the surface and bottom of the lake as heat reservoirs, what would be its efficiency?
(b) If the town needs about $1.0 \times 10^{8} \mathrm{~W}$ of power to be supplied by the lake, how many $\mathrm{m}^{3}$ of water does the heat engine use per second? (c) The surface area of the lake is $8.0 \times 10^{7} \mathrm{~m}^{2}$ and the average incident intensity (over $24 \mathrm{~h}$ ) of the sunlight is $200 \mathrm{~W} / \mathrm{m}^{2}$. Can the lake supply enough heat to meet the town's energy needs with this method?

Matthew Muscat

Numerade Educator

Problem 78

In a heat engine, $3.00 \mathrm{~mol}$ of a monatomic ideal gas, initially at $4.00$ atm of pressure, undergoes an isothermal expansion, increasing its volume by a factor of $9.50$ at a constant temperature of $650.0 \mathrm{~K}$. The gas is then compressed at a constant pressure to its original volume. Finally, the pressure is increased at constant volume back to the original pressure. (a) Draw a $P V$ diagram of this three-step heat engine. (b) For each step of this process, calculate the work done on the gas, the change in internal energy, and the heat transferred into the gas. (c) What is the efficiency of this engine?

Matthew Muscat

Numerade Educator