College Physics

Jerry D. Wilson, Anthony J. Buffa, Bo Lou

Chapter 12

Thermodynamics - all with Video Answers

Educators

Chapter Questions

Problem 1

While playing in a tennis match, you lost $6.5 \times 10^{5} \mathrm{~J}$ of heat, and your internal energy also decreased by $1.2 \times 10^{6} \mathrm{~J}$. How much work did you do in the match?

Shahab Ullah

Shahab Ullah

Numerade Educator

Problem 2

A rigid container contains $1.0 \mathrm{~mol}$ of an ideal gas that slowly receives $2.0 \times 10^{4} \mathrm{~J}$ of heat. (a) The work done by the gas is (1) positive, (2) zero, (3) negative. Why? (b) What is the change in the internal energy of the gas?

Shahab Ullah

Numerade Educator

Problem 3

A quantity of ideal gas goes through an isothermal process and does 400 J of net work. (a) The internal energy of the gas is (1) higher than, (2) the same as, (3) less than when it started. Why? (b) Is a net amount of heat added to or removed from the system, and how much is involved?

Shahab Ullah

Numerade Educator

Problem 4

An ideal gas goes through a thermodynamic process in which $500 \mathrm{~J}$ of work is done on the gas and the gas loses $300 \mathrm{~J}$ of heat. What is the change in internal energy of the gas?

Shahab Ullah

Numerade Educator

Problem 5

While doing 500 J of work, an ideal gas expands adiabatically to 1.5 times its initial volume. (a) The temperature of the gas (1) increases, (2) remains the same, (3) decreases. Why? (b) What is the change in the internal energy of the gas?

Shahab Ullah

Numerade Educator

Problem 6

An ideal gas expands from $1.0 \mathrm{~m}^{3}$ to $3.0 \mathrm{~m}^{3}$ at atmospheric pressure while absorbing $5.0 \times 10^{5} \mathrm{~J}$ of heat in the process. (a) The temperature of the system(1) increases, (2) stays the same, (3) decreases. Explain. (b) What is the change in internal energy of the system?

Shahab Ullah

Numerade Educator

Problem 7

An ideal gas is under an initial pressure of $2.45 \times 10^{4} \mathrm{~Pa}$ and occupies a volume of $0.20 \mathrm{~m}^{3} .$ The slow addition of $8.4 \times 10^{3} \mathrm{~J}$ of heat to this gas causes it to expand isobarically to a volume of $0.40 \mathrm{~m}^{3}$. (a) How much work is done by the gas in the process? (b) Does the internal energy of the gas change? If so, by how much?

Shahab Ullah

Numerade Educator

Problem 8

An Olympic weight lifter lifts $145 \mathrm{~kg}$ a vertical distance of $2.1 \mathrm{~m}$. When he does $\mathrm{so}, 6.0 \times 10^{4} \mathrm{~J}$ of heat is transferred to air through perspiration. Does he gain or lose internal energy and how much?

Shahab Ullah

Numerade Educator

Problem 9

An ideal gas is taken through the reversible processes shown in $>$ Fig. $12.21 .$ (a) Is the overall change in the internal energy of the gas (1) positive, (2) zero, or (3) negative? Explain. (b) In terms of state variables $p$ and $V$, how much work is done by or on the gas, and
(c) what is the net heat transfer in the overall process?

Satpal Satpal

Numerade Educator

Problem 10

A fixed quantity of gas undergoes the reversible changes illustrated in the $p-V$ diagram in Fig. $12.22 .$ How much work is done in each process?

Satpal Satpal

Numerade Educator

Problem 11

Suppose that after the final process in Fig. 12.22 (see Exercise 10$)$, the pressure of the gas is decreased isometrically from $1.0 \times 10^{5} \mathrm{~Pa}$ to $0.70 \times 10^{5} \mathrm{~Pa}$, and then the gas is compressed isobarically from $1.0 \mathrm{~m}^{3}$ to $0.80 \mathrm{~m}^{3}$. What is the total work done in all of these processes, including 1 through $5 ?$

Satpal Satpal

Numerade Educator

Problem 12

A gas is enclosed in a cylindrical piston with a 12.0-cm radius. Heat is slowly added to the gas while the pressure is maintained at $1.00 \mathrm{~atm} .$ During the process, the piston moves $6.00 \mathrm{~cm} .$ (a) This is an (1) isothermal, (2) isobaric, (3) adiabatic process. Explain. (b) If the heat transferred to the gas during the expansion is $420 \mathrm{~J},$ what is the change in the internal energy of the gas?

Satpal Satpal

Numerade Educator

Problem 13

$2.0 \mathrm{~mol}$ of an ideal gas expands isothermally from a volume of $20 \mathrm{~L}$ to $40 \mathrm{~L}$ at $20{ }^{\circ} \mathrm{C}$. (a) The work done by the gas is (1) positive, (2) negative, (3) zero. Explain. (b) What is the magnitude of the work?

Satpal Satpal

Numerade Educator

Problem 14

A monatomic ideal gas $(\gamma=1.67)$ is compressed adiabatically from a pressure of $1.00 \times 10^{5} \mathrm{~Pa}$ and volume of $240 \mathrm{~L}$ to a volume of $40.0 \mathrm{~L}$. (a) What is the final pressure of the gas? (b) How much work is done on the gas?

Satpal Satpal

Numerade Educator

Problem 15

An ideal gas sample expands isothermally by tripling its volume and doing $5.0 \times 10^{4} \mathrm{~J}$ of work at $40^{\circ} \mathrm{C} .$ (a) How many moles of gas are there in the sample? (b) Was heat added to or removed from the sample, and how much?

Satpal Satpal

Numerade Educator

Problem 16

The temperature of $2.0 \mathrm{~mol}$ of ideal gas is increased from $150^{\circ} \mathrm{C}$ to $250^{\circ} \mathrm{C}$ by two different processes. In process $A, 2500$ J of heat is added to the gas; in process $B, 3000$ J of heat is added. (a) In which case is more work done: (1) process $A,(2)$ process $B,$ or (3) the same amount of work is done? Explain. [Hint: See Eq. $10.16 .]$ (b) Calculate the change in internal energy and work done for each process.

Satpal Satpal

Numerade Educator

Problem 17

One handred moles of a monatomic gas is compressed as shown on the $p-V$ diagram in $v$ Fig. $12.23 .$ (a) Is the work done by the gas (1) positive, (2) zero, or (3) negative? Why? (b) What is the work done by the gas? (c) What is the change in temperature of the gas? (d) What is the change in internal energy of the gas? (e) How much heat is involved in the process?

Linda Winkler

Numerade Educator

Problem 18

One mole of an ideal gas is taken through the cyclio process shown in Fig. $12.24 .$ (a) Compute the work involved for each of the four processes. (b) Find $\Delta U, W$, and $Q$ for the complete cycle. (c) What is $T_{3}$ ?

Linda Winkler

Numerade Educator

Problem 19

What is the change in entropy of mercury vapor $\left(L_{\mathrm{v}}=2.7 \times 10^{5} \mathrm{~J} / \mathrm{kg}\right)$ when $0.50 \mathrm{~kg}$ of it condenses to $\mathrm{a}$ liquid at its boiling point of $357^{\circ} \mathrm{C} ?$

Shahab Ullah

Numerade Educator

Problem 20

$2.0 \mathrm{~kg}$ of ice melts completely into liquid water at $0^{\circ} \mathrm{C}$. (a) The change in entropy of the ice (water) in this process is (1) positive, (2) zero, (3) negative. Explain. (b) What is the change in entropy of the ice (water)?

Satpal Satpal

Numerade Educator

Problem 21

A process involves $1.0 \mathrm{~kg}$ of steam condensing to water at $100^{\circ} \mathrm{C}$. (a) The change in entropy of the steam (water) is (1) positive, (2) zero, (3) negative. Why? (b) What is the change in entropy of the steam (water)?

Shahab Ullah

Numerade Educator

Problem 22

During a liquid-to-solid phase change of a substance, its change in entropy is $-4.19 \times 10^{3} \mathrm{~J} / \mathrm{K}$. If $1.67 \times 10^{6} \mathrm{~J}$ of heat is removed in the process, what is the freezing point of the substance in degrees Celsius?

Shahab Ullah

Numerade Educator

Problem 23

In an isothermal expansion at $27^{\circ} \mathrm{C},$ an ideal gas does 60 J of work. What is the change in entropy of the gas?

Shahab Ullah

Numerade Educator

Problem 24

One mole of an ideal gas undergoes an isothermal compression at $0^{\circ} \mathrm{C},$ and $7.5 \times 10^{3} \mathrm{~J}$ of work is done in compressing the gas. (a) Will the entropy of the gas (1) increase, (2) remain the same, or (3) decrease? Why? (b) What is the change in entropy of the gas?

Satpal Satpal

Numerade Educator

Problem 25

A quantity of an ideal gas undergoes an isother-mal expansion at $20^{\circ} \mathrm{C}$ and does $3.0 \times 10^{3} \mathrm{~J}$ of work on its surroundings in the process. (a) Will the entropy of the gas (1) increase, (2) remain the same, or (3) decrease? Explain. (b) What is the change in the entropy of the gas?

Satpal Satpal

Numerade Educator

Problem 26

In the winter, heat from a house with an inside temperature of $18^{\circ} \mathrm{C}$ leaks out at a rate of $2.0 \times 10^{4} \mathrm{~J} / \mathrm{s}$. The outside temperature is $0^{\circ} \mathrm{C}$. (a) What is the change in entropy per second of the house? (b) What is the total change in entropy per second of the house-outside system?

Shahab Ullah

Numerade Educator

Problem 27

An isolated system consists of two very large thermal reservoirs at constant temperatures of $100^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$. Assume the reservoirs made contact and $1000 \mathrm{~J}$ of heat flew from the cold reservoir to the hot reservoir spontaneously. (a) The total change in entropy of the isolated system (both reservoirs) would be (1) positive, (2) zero, (3) negative. Explain.
(b) Calculate the total change in entropy of this isolated system.

Satpal Satpal

Numerade Educator

Problem 28

Two large heat reservoirs at temperatures $200^{\circ} \mathrm{C}$ and $60^{\circ} \mathrm{C}$, respectively, are brought into thermal contact, and $1.50 \times 10^{3} \mathrm{~J}$ of heat spontaneously flows from one to the other with no significant temperature change.
(a) The change in the entropy of the two-reservoir system is (1) positive, (2) zero, (3) negative. Explain. (b) Calculate the change in the entropy of the two-reservoir system.

Satpal Satpal

Numerade Educator

Problem 29

A system goes from state 1 to state 3 as shown on the $T-S$ diagram in Fig. $12.25 .$ (a) The heat transfer for the process going from state 2 to state 3 is (1) positive, (2) zero, (3) negative. Explain. (b) Calculate the total heat transferred in going from state 1 to state 3.

Satpal Satpal

Numerade Educator

Problem 30

Suppose that the system described by the $T-S$ diagram in Fig. 12.25 is returned to its original state, state 1 , by a reversible process depicted by a straight line from state 3 to state $1 .$ (a) The change in entropy of the system for this overall cyclic process is (1) positive,
(2) zero,
(3) negative. Explain. (b) How much heat is transferred in the cyclic process? [Hint: See Example $12.6 .]$

Satpal Satpal

Numerade Educator

Problem 31

A 50.0 -g ice cube at $0^{\circ} \mathrm{C}$ is placed in $500 \mathrm{~mL}$ of water at $20^{\circ} \mathrm{C}$. Estimate the change in entropy (after all the ice has melted) (a) for the ice, (b) for the water, and (c) for the ice-water system.

Linda Winkler

Numerade Educator

Problem 32

If an engine does $200 \mathrm{~J}$ of net work and exhausts $800 \mathrm{~J}$ of heat per cycle, what is its thermal efficiency?

Shahab Ullah

Numerade Educator

Problem 33

A gasoline engine has a thermal efficiency of $28 \%$. If the engine absorbs $2000 \mathrm{~J}$ of heat per cycle, $(\mathrm{a})$ what is the net work output per cycle? (b) How much heat is exhausted per cycle?

Shahab Ullah

Numerade Educator

Problem 34

A heat engine with a thermal efficiency of $20 \%$ does $500 \mathrm{~J}$ of net work each cycle. How much heat per cycle is lost to the low-temperature reservoir?

Shahab Ullah

Numerade Educator

Problem 35

An internal combustion engine with a thermal efficiency of $15.0 \%$ absorbs $1.75 \times 10^{5} \mathrm{~J}$ of heat from the hot reservoir. How much heat is lost by the engine in each cycle?

Shahab Ullah

Numerade Educator

Problem 36

The heat output of a particular engine is $7.5 \times 10^{3} \mathrm{~J}$ per cycle, and the net work out is $4.0 \times 10^{3} \mathrm{~J}$ per cycle. (a) The heat input is (1) less than $4.0 \times 10^{3} \mathrm{~J},$ (2) between $4.0 \times 10^{3} \mathrm{~J}$ and $7.5 \times 10^{3} \mathrm{~J},$ (3) greater than $7.5 \times 10^{3} \mathrm{~J}$ Explain. (b) What is the heat input and thermal efficiency of the engine?

Shahab Ullah

Numerade Educator

Problem 37

A gasoline engine burns fuel that releases $3.3 \times 10^{8} \mathrm{~J}$ of heat per hour. (a) What is the energy input during a 2.0-h period? (b) If the engine delivers $25 \mathrm{~kW}$ of power during this time, what is its thermal efficiency?

Shahab Ullah

Numerade Educator

Problem 38

A steam engine is to have its thermal efficiency improved from $8.00 \%$ to $10.0 \%$ while continuing to produce 4500 J of useful work each cycle. (a) Does the ratio of the heat output to heat input (1) increase, (2) remain the same, or (3) decrease? Why? (b) What is the change in $Q_{c} / Q_{h}$ in this example?

Satpal Satpal

Numerade Educator

Problem 39

An engineer redesigns a heat engine and improves its thermal efficiency from $20 \%$ to $25 \% .$ (a) Does the ratio of the heat input to heat output (1) increase, (2) remain the same, or (3) decrease? Explain. (b) What is the engine's change in $Q_{\mathrm{h}} / Q_{\mathrm{c}}$ ?

Linda Winkler

Numerade Educator

Problem 40

When running, a refrigerator exhausts heat to the kitchen at a rate of $10 \mathrm{~kW}$ when the required input work is done at a rate of $3.0 \mathrm{~kW}$. (a) At what rate is heat removed from its cold interior? (b) What is the COP of the refrigerator?

Shahab Ullah

Numerade Educator

Problem 41

A refrigerator with a $\mathrm{COP}$ of 2.2 removes $4.2 \times 10^{5} \mathrm{~J}$ of heat from its interior each cycle. (a) How much heat is exhausted each cycle? (b) What is the total work input in joules for 10 cycles?

Shahab Ullah

Numerade Educator

Problem 42

An air conditioner has a COP of $2.75 .$ What is the power rating of the unit if it is to remove $1.00 \times 10^{7} \mathrm{~J}$ of heat from a house interior in $20 \mathrm{~min} ?$

Shahab Ullah

Numerade Educator

Problem 43

A heat pump removes $2.2 \times 10^{3} \mathrm{~J}$ of heat from the outdoors and delivers $4.3 \times 10^{3} \mathrm{~J}$ of heat to the inside of a house each cycle. (a) How much work is required per cycle? (b) What is the COP of this pump?

Shahab Ullah

Numerade Educator

Problem 44

A steam engine has a thermal efficiency of $15.0 \% .$ If its heat input for each cycle is supplied by the condensation of $8.00 \mathrm{~kg}$ of steam at $100{ }^{\circ} \mathrm{C}$. (a) what is the net work output per cycle, and (b) how much heat is lost to the surroundings in each cycle?

Shahab Ullah

Numerade Educator

Problem 45

A coal-fired power plant produces $900 \mathrm{MW}$ of electric power and operates at a thermal efficiency of $25 \%$
(a) What is the input heat rate from the burning coal?
(b) What is the rate of heat discharge from the plant?
(c) Water at $15^{\circ} \mathrm{C}$ from a nearby river is used to cool the discharged heat. If the cooling water is not to exceed a temperature of $40{ }^{\circ} \mathrm{C},$ how many gallons per minute of the cooling water is required?

Satpal Satpal

Numerade Educator

Problem 46

A gasoline engine has a thermal efficiency of $25.0 \%$. If heat is expelled from the engine at a rate of $1.50 \times 10^{6} \mathrm{~J} / \mathrm{h},$ how long does the engine take to perform a task that requires an amount of work of $1.5 \times 10^{6} \mathrm{~J} ?$

Shahab Ullah

Numerade Educator

Problem 47

A four-stroke engine runs on the Otto cycle. It delivers 150 hp at 3600 rpm. (a) How many cycles are in 1 min? (b) If the thermal efficiency of the engine is $20 \%$ what is the heat input per minute? (c) How much heat is wasted (per minute) to the environment?

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 48

A Carnot engine has an efficiency of $35 \%$ and takes in heat from a high-temperature reservoir at $178^{\circ} \mathrm{C}$. What is the Celsius temperature of the engine's low-temperature reservoir?

Nishant Kumar

Numerade Educator

Problem 49

A steam engine operates between $100^{\circ} \mathrm{C}$ and $20^{\circ} \mathrm{C}$. What is the Carnot efficiency of the ideal engine that operates between these temperatures?

Shahab Ullah

Numerade Educator

Problem 50

It has been proposed that temperature differences in the ocean could be used to run a heat engine to generate electricity. In tropical regions, the water temperature is about $25^{\circ} \mathrm{C}$ at the surface and about $5^{\circ} \mathrm{C}$ at very deep depths. (a) What would be the maximum theoretical efficiency of such an engine? (b) Would a heat engine with such a low efficiency be practical? Explain.

Shahab Ullah

Numerade Educator

Problem 51

What is the Celsius temperature of the hot reservoir of a Carnot engine that is $32 \%$ efficient and has a $20^{\circ} \mathrm{C}$ cold reservoir?

Shahab Ullah

Numerade Educator

Problem 52

An engineer wants to run a heat engine with an efficiency of $40 \%$ between a high-temperature reservoir at $300^{\circ} \mathrm{C}$ and a low-temperature reservoir. What is the maximum Celsius temperature of the low-temperature reservoir?

Shahab Ullah

Numerade Educator

Problem 53

A Carnot engine with an efficiency of $40 \%$ operates with a low-temperature reservoir at $40^{\circ} \mathrm{C}$ and exhausts $1200 \mathrm{~J}$ of heat each cycle. What are (a) the heat input per cycle and (b) the Celsius temperature of the hightemperature reservoir?

Shahab Ullah

Numerade Educator

Problem 54

A Carnot engine takes $2.7 \times 10^{4} \mathrm{~J}$ of heat per cycle from a high-temperature reservoir at $320{ }^{\circ} \mathrm{C}$ and exhausts some of it to a low-temperature reservoir at $120^{\circ} \mathrm{C}$ How much net work is done by the engine per cycle?

Shahab Ullah

Numerade Educator

Problem 55

A Carnot engine takes in heat from a reservoir at $350^{\circ} \mathrm{C}$ and has an efficiency of $35 \%$. The exhaust temperature is not changed and the efficiency is increased to $40 \%$ (a) The temperature of the hot reservoir is (1) lower than (2) equal to, (3) higher than $350^{\circ} \mathrm{C}$. Explain. (b) What is the new Celsius temperature of the hot reservoir?

Shahab Ullah

Numerade Educator

Problem 56

An inventor claims to have created a heat engine that produces $10.0 \mathrm{~kW}$ of power for a $15.0-\mathrm{kW}$ heat input while operating between reservoirs at $27^{\circ} \mathrm{C}$ and $427^{\circ} \mathrm{C}$. (a) Is this claim valid? (b) To produce $10.0 \mathrm{~kW}$ of power, what is the minimum heat input required?

Shahab Ullah

Numerade Educator

Problem 57

An inventor claims to have developed a heat engine that, each cycle, takes in $5.0 \times 10^{5} \mathrm{~J}$ of heat from a hightemperature reservoir at $400^{\circ} \mathrm{C}$ and exhausts $2.0 \times 10^{5} \mathrm{~J}$ to the surroundings at $125^{\circ} \mathrm{C}$. Would you invest your money in the production of this engine? Explain.

Shahab Ullah

Numerade Educator

Problem 58

A heat engine operates at a thermal efficiency that is $45 \%$ of the Carnot efficiency. If the temperatures of the high-temperature and low-temperature reservoirs are $400^{\circ} \mathrm{C}$ and $50^{\circ} \mathrm{C},$ respectively, what are the Carnot efficiency and the thermal efficiency of the engine?

Shahab Ullah

Numerade Educator

Problem 59

A heat engine's thermal efficiency is $70.0 \%$ of the Carnot efficiency of an engine operating between temperatures of $80^{\circ} \mathrm{C}$ and $375^{\circ} \mathrm{C} .$ (a) What is the Carnot efficiency of the heat engine? (b) If the heat engine absorbs heat at a rate of $50 \mathrm{~kW}$, at what rate is heat exhausted?

Shahab Ullah

Numerade Educator

Problem 60

In each cycle, a Carnot engine takes 800 J of heat from a high-temperature reservoir and discharges $600 \mathrm{~J}$ to a low-temperature reservoir. What is the ratio of the temperature of the high-temperature reservoir to that of the low-temperature reservoir?

Shahab Ullah

Numerade Educator

Problem 61

A Carnot engine operating between reservoirs at $27^{\circ} \mathrm{C}$ and $227^{\circ} \mathrm{C}$ does $1500 \mathrm{~J}$ of work in each cycle. (a) The change in entropy for the engine for each cycle is (1) negative, (2) zero, (3) positive. Why? (b) What is the heat input of the engine?

Shahab Ullah

Numerade Educator

Problem 62

The autoignition temperature of a fuel is defined as the temperature at which a fuel-air mixture would selfexplode and ignite. Thus, it sets an upper limit on the temperature of the hot reservoir in an automobile engine. The autoignition temperatures for commonly available gasoline and diesel fuel are about $495^{\circ} \mathrm{F}$ and $600^{\circ} \mathrm{F}$, respectively. What are the maximum Carnot efficiencies of a gasoline engine and a diesel engine if the cold reservoir temperature is $40^{\circ} \mathrm{C} ?$

Shahab Ullah

Numerade Educator

Problem 63

Because of limitations on materials, the maximum temperature of the superheated steam used in a turbine for the generation of electricity is about $540{ }^{\circ} \mathrm{C} .(\mathrm{a})$ If the steam condenser operates at $20^{\circ} \mathrm{C},$ what is the maximum Carnot efficiency of a steam turbine generator? (b) The actual efficiency of such generators is about $35 \%$ to $40 \% .$ What does this range tell you?

Shahab Ullah

Numerade Educator

Problem 64

The working substance of a cyclic heat engine is $0.75 \mathrm{~kg}$ of an ideal gas. The cycle consists of two isobaric processes and two isometric processes, as shown in FFig. $12.26 .$ What would be the efficiency of a Carnot engine operating with the same high-temperature and low-temperature reservoirs?

Linda Winkler

Numerade Educator

Problem 65

Equation 12.15 shows that the greater the temperature difference between the reservoirs of a heat engine, the greater the engine's Carnot efficiency. Suppose you had the choice of raising the temperature of the high-temperature reservoir by a certain number of kelvins or lowering the temperature of the low-temperature reservoir by the same number of kelvins. (a) To produce the largest increase in efficiency, you should choose (1) to raise the high-temperature reservoir, (2) to lower the low-temperature reservoir, (3) both 1 and 2 produce the same change in efficiency, so it does not matter which you choose. Explain. (b) Prove your answer to part (a) mathematically.

Linda Winkler

Numerade Educator

Problem 66

There is a Carnot coefficient of performance $\left(\mathrm{COP}_{\mathrm{C}}\right)$ for an ideal, or Carnot, refrigerator. (a) Show that this quantity is given by $$\mathrm{COP}_{\mathrm{C}}=\frac{T_{\mathrm{c}}}{T_{\mathrm{h}}-T_{\mathrm{c}}}$$ (b) What does this tell you about adjusting the temperatures for the maximum COP of a refrigerator? (Can you guess the equation for the $\mathrm{COP}_{\mathrm{C}}$ for a heat pump?)

Linda Winkler

Numerade Educator

Problem 67

A salesperson tells you that a new refrigerator with a high COP removes $2.6 \times 10^{3} \mathrm{~J}$ (each cycle) from the inside of the refrigerator at $5.0^{\circ} \mathrm{C}$ and expels $2.8 \times 10^{3} \mathrm{~J}$ into the $30^{\circ} \mathrm{C}$ kitchen. (a) What is the refrigerator's COP? (b) Is this scenario possible? Justify your answer. (See Exercise 66.)

Shahab Ullah

Numerade Educator

Problem 68

An ideal heat pump is equivalent to a Carnot engine running in reverse. (a) Show that the Carnot COP of the heat pump is $\mathrm{COP}_{\mathrm{C}}=\frac{1}{\varepsilon_{\mathrm{C}}}$ where $\varepsilon_{C}$ is the Carnot efficiency of the heat engine. (b) If a Carnot engine has an efficiency of $40 \%,$ what would be the $\mathrm{COP}_{\mathrm{C}}$ when it runs in reverse as a heat pump? (See Exercise $66 .)$

Satpal Satpal

Numerade Educator

Problem 69

A heat engine with a thermal efficiency of $25 \%$ is used to hoist $2.5-\mathrm{kg}$ bricks to an elevation of $3.0 \mathrm{~m}$. If the engine expels heat to the environment at a rate of $1.2 \times 10^{6} \mathrm{~J} / \mathrm{h}$ how many bricks can the engine hoist in $2.0 \mathrm{~h} ?$

Shahab Ullah

Numerade Educator

Problem 70

When cruising at $75 \mathrm{mi} / \mathrm{h}$ on a highway, a car's engine develops 45 hp. If this engine has a thermodynamic efficiency of $25 \%$ and 1 gal of gasoline has an energy content of $1.3 \times 10^{8} \mathrm{~J}$, what is the fuel efficiency (in miles per gallon) of this car?

Satpal Satpal

Numerade Educator

Problem 71

A gram of water (volume of $1.00 \mathrm{~cm}^{3}$ ) at $100{ }^{\circ} \mathrm{C}$ is converted to $1.67 \times 10^{3} \mathrm{~cm}^{3}$ of steam at atmospheric pressure. What is the change in the internal energy of the water (steam)?

Shahab Ullah

Numerade Educator

Problem 72

In a highly competitive game, a basketball player can produce $300 \mathrm{~W}$ of power. Assuming the efficiency of the player's "engine" is $15 \%$ and heat dissipates primarily through the evaporation of perspiration, what mass of perspiration is evaporated per hour?

Linda Winkler

Numerade Educator

Problem 73

A Carnot engine is to produce 100 J of work per cycle. If $300 \mathrm{~J}$ of heat is exhausted to a $27{ }^{\circ} \mathrm{C}$ cold reservoir per cycle, what is the change in entropy of the hot reservoir per cycle?

Shahab Ullah

Numerade Educator

Problem 74

A quantity of an ideal gas at an initial pressure of 2.00 atm undergoes an adiabatic expansion to atmospheric pressure. What is the ratio of the final temperature to the initial temperature of the gas?

Satpal Satpal

Numerade Educator

Problem 75

A 100 -MW power generating plant has an efficiency of $40 \%$. If water is used to carry off the wasted heat and the temperature of the water is not to increase by more than $10^{\circ} \mathrm{C},$ what mass of water must flow through the plant each second?

Linda Winkler

Numerade Educator

Problem 76

An ice machine is to convert $10^{\circ} \mathrm{C}$ water to $0^{\circ} \mathrm{C}$ ice. If the machine has a COP of 2.0 and consumes electrical power at a rate of $1.0 \mathrm{~kW}$, how much ice can it make in $1.0 \mathrm{~h} ?$

Satpal Satpal

Numerade Educator