Physics

John D. Cutnell, Kenneth W. Johnson

Chapter 15

Thermodynamics - all with Video Answers

Educators

+ 5 more educators

Chapter Questions

Problem 1

In moving out of a dormitory at the end of the semester, a student does $1.6 \times 10^{4} \mathrm{J}$ of work. In the process, his internal energy decreases by $4.2 \times 10^{4}$ J. Determine each of the following quantities (including the algebraic sign): (a) $W$ (b) $\Delta U$ (c) $Q$

Yaqub Khan

Yaqub Khan

Numerade Educator

Problem 2

The internal energy of a system changes because the system gains 165 $\mathrm{J}$ of heat and performs 312 $\mathrm{J}$ of work. In returning to its initial state, the system loses 114 $\mathrm{J}$ of heat. During this return process, (a) what work is involved, and $(\mathrm{b})$ is the work done by the system or on the system?

Yaqub Khan

Numerade Educator

Problem 3

A system does 164 $\mathrm{J}$ of work on its environment and gains 77 $\mathrm{J}$ of heat in the process. Find the change in the internal energy of $(\text { a ) the }$ system and (b) the environment.

Yaqub Khan

Numerade Educator

Problem 4

A system does $4.8 \times 10^{4} \mathrm{J}$ of work , and $7.6 \times 10^{4} \mathrm{J}$ of heat flows into the system during the process. Find the change in the internal energy of the system.

Yaqub Khan

Numerade Educator

Problem 5

In a game of football outdoors on a cold day, a player will begin to feel exhausted after using approximately $8.0 \times 10^{5} \mathrm{J}$ of internal energy. (a) One player, dressed too lightly for the weather, has to leave the game after losing $6.8 \times 10^{5} \mathrm{J}$ of heat. How much work has he done? (b) Another player, wearing clothes that offer better protection against heat loss, is able to remain in the game long enough to do $2.1 \times 10^{5} \mathrm{J}$ of work. What is the magnitude of the heat that he has lost?

Yaqub Khan

Numerade Educator

Problem 6

Three moles of an ideal monatomic gas are at a temperature of 345 $\mathrm{K}$ . Then, 2438 $\mathrm{J}$ of heat is added to the gas, and 962 $\mathrm{J}$ of work is done on it. What is the final temperature of the gas?

Yaqub Khan

Numerade Educator

Problem 7

In exercising, a weight lifter loses 0.150 $\mathrm{kg}$ of water through evaporation, the heat required to evaporate the water coming from the weight lifter's body. The work done in lifting weights is $1.40 \times 10^{5} \mathrm{J}$ (a) Assuming that the latent heat of vaporization of perspiration is $2.42 \times 10^{6} \mathrm{J} / \mathrm{kg}$ find the change in the internal energy of the weight lifter. $(\mathbf{b})$ Determine the minimum number of nutritional Calories of food $(1 \text { nutritional Calorie }=4186 \mathrm{J})$ that must be consumed to replace the loss of internal energy.

Yaqub Khan

Numerade Educator

Problem 8

A system undergoes a two-step process. In the first step, the internal energy of the system increases by 228 $\mathrm{J}$ when 166 $\mathrm{J}$ of work is done on the system. In the second step, the internal energy of the system increases by 115 $\mathrm{J}$ when 177 $\mathrm{J}$ of work is done on the system. For the overall process, find the heat. What type of process is the overall process?
Explain.

Yaqub Khan

Numerade Educator

Problem 9

When a .22 -caliber rifle is fired, the expanding gas from the burning gunpowder creates a pressure behind the bullet. This pressure causes the force that pushes the bullet through the barrel. The barrel has a length of 0.61 $\mathrm{m}$ and an opening whose radius is $2.8 \times 10^{-3} \mathrm{m} . \mathrm{A}$ bullet (mass $=2.6 \times 10^{-3} \mathrm{kg}$ ) has a speed of 370 $\mathrm{m} / \mathrm{s}$ after passing through this barrel. Ignore friction and determine the average pressure
of the expanding gas.

Yaqub Khan

Numerade Educator

Problem 10

A system gains 2780 $\mathrm{J}$ of heat at a constant pressure of $1.26 \times 10^{5} \mathrm{Pa}$ , and its internal energy increases by 3990 $\mathrm{J}$ . What is the change in the volume of the system, and is it an increase or a decrease?

Yaqub Khan

Numerade Educator

Problem 11

A system gains 1500 $\mathrm{J}$ of heat, while the internal energy of the system increases by 4500 $\mathrm{J}$ and the volume decreases by 0.010 $\mathrm{m}^{3}$ . Assume that the pressure is constant and find its value.

Yaqub Khan

Numerade Educator

Problem 12

The volume of a gas is changed along the curved line between $A$ and $B$ in the drawing. Do not assume that the curved line is an isotherm or that the gas is ideal. (a) Find the magnitude of the
work for the process, and (b) deter- mine whether the work is positive or negative.

Supratim Pal

Numerade Educator

Problem 13

(a) Using the data presented in the accompanying pressure-volume graph, estimate the magnitude
of the work done when the system changes from $A$ to $B$ to $C$ along the path shown. (b) Determine
whether the work is done by the system or on the system and, hence, whether the work is positive or
negative.

Vishal Gupta

Numerade Educator

Problem 14

Sections 14.2 and 14.3 provide useful information for this problem. When a monatomic ideal gas expands at a constant pressure of $2.6 \times 10^{5} \mathrm{Pa}$ , the volume of the gas increases by $6.2 \times 10^{-3} \mathrm{m}^{3} .$ (a) Determine the heat that flows into or out of the gas. (b) Specify the direction of the flow.

Yaqub Khan

Numerade Educator

Problem 15

A gas is contained in a chamber such as that in Figure $15.4 .$ Suppose that the region outside the chamber is evacuated and the total mass of the block and the movable piston is 135 $\mathrm{kg}$ . When 2050 $\mathrm{J}$ of heat flows into the gas, the internal energy of the gas increases by 1730 $\mathrm{J}$ . What is the distance $s$ through which the piston rises?

Yaqub Khan

Numerade Educator

Problem 16

A piece of aluminum has a volume of $1.4 \times 10^{-3} \mathrm{m}^{3} .$ The coefficient of volume expansion for aluminum is $\beta=69 \times 10^{-6}\left(\mathrm{C}^{\circ}\right)^{-1}$ . The temperature of this object is raised from 20 to $320^{\circ} \mathrm{C} .$ How much work is
done by the expanding aluminum if the air pressure is $1.01 \times 10^{5} \mathrm{Pa} ?$

Yaqub Khan

Numerade Educator

Problem 17

Refer to Multiple-Concept Example 3 to see how the concepts pertinent to this problem are used. The pressure of a gas remains constant while the temperature, volume, and internal energy of the gas increase by $53.0 \mathrm{C}^{\circ}, 1.40 \times 10^{-3} \mathrm{m}^{3},$ and 939 $\mathrm{J}$ , respectively. The mass of the gas is $24.0 \mathrm{g},$ and its specific heat capacity is 1080 $\mathrm{J} / \mathrm{kg} \cdot \mathrm{C}^{\circ}$ ). Determine the pressure.

Yaqub Khan

Numerade Educator

Problem 18

Refer to the drawing that accompanies Problem $13 .$ When a system changes from $A$ to $B$ along the path shown on the pressure-versus-volume graph, it gains 2700 $\mathrm{J}$ of heat. What is the change in the internal energy of the system?

Yaqub Khan

Numerade Educator

Problem 19

Water is heated in an open pan where the air pressure is one atmosphere. The water remains a liquid, which expands by a small amount as it is heated. Determine the ratio of the work done by the water to the heat absorbed by the water.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 20

Six grams of helium (molecular mass $=4.0 \mathrm{u} )$ expand isothermally at 370 $\mathrm{K}$ and does 9600 $\mathrm{J}$ of work. Assuming that helium is an ideal gas, determine the ratio of the final volume of the gas to the initial volume.

Yaqub Khan

Numerade Educator

Problem 21

Five moles of a monatomic ideal gas expand adiabatically, and its temperature decreases from 370 to 290 $\mathrm{K}$ . Determine $\quad$ (a) the work done (including the algebraic sign) by the gas, and (b) the change in its internal energy.

Yaqub Khan

Numerade Educator

Problem 22

Three moles of neon expand isothermally to 0.250 from 0.100 $\mathrm{m}^{3}$ Into the gas flows $4.75 \times 10^{3} \mathrm{J}$ of heat. Assuming that neon is an ideal gas, find its temperature.

Yaqub Khan

Numerade Educator

Problem 23

The temperature of a monatomic ideal gas remains constant during a process in which 4700 $\mathrm{J}$ of heat flows out of the gas. How much work (including the proper $+$ or $-$ sign ) is done?

Yaqub Khan

Numerade Educator

Problem 24

One-half mole of a monatomic ideal gas expands adiabatically and does 610 $\mathrm{J}$ of work. By how many kelvins does its temperature change? Specify whether the change is an increase or a decrease.

Yaqub Khan

Numerade Educator

Problem 25

A monatomic ideal gas has an initial temperature of 405 $\mathrm{K}$ . This gas expands and does the same amount of work whether the expansion is adiabatic or isothermal. When the expansion is adiabatic, the final temperature of the gas is 245 $\mathrm{K}$ . What is the ratio of the final to the initial volume when the expansion is isothermal?

Yaqub Khan

Numerade Educator

Problem 26

Heat is added isothermally to 2.5 mol of a monatomic ideal gas. The temperature of the gas is 430 $\mathrm{K}$ . How much heat must be added to make the volume of the gas double?

Yaqub Khan

Numerade Educator

Problem 27

A diesel engine does not use spark plugs to ignite the fuel and air in the cylinders. Instead, the temperature required to ignite the fuel occurs because the pistons compress the air in the cylinders. Suppose that air at an initial temperature of $21^{\circ} \mathrm{C}$ is compressed adiabatically to
a temperature of $688^{\circ} \mathrm{C}$ . Assume the air to be an ideal gas for which $\gamma=\frac{7}{5} .$ Find the compression ratio, which is the ratio of the initial volume to the final volume.

Yaqub Khan

Numerade Educator

Problem 28

A monatomic ideal gas expands from point $A$ to point $B$ along the path shown in the drawing. (a) Determine the work done by the gas. (b) The temperature of the gas at point $A$ is 185 $\mathrm{K}$ . What is its temperature at point $B$ ? (c) How much heat has been added to or removed from the
gas during the process?

Dading Chen

Numerade Educator

Problem 29

The drawing refers to one mole of a monatomic ideal gas and shows a process that has four steps, two isobaric $(A \text { to } B, C \text { to } D)$ and two isochoric $(B \text { to } C, D \text { to } A) .$ Complete the following table by calculating $\Delta U, W,$ and $Q$ (including the algebraic signs) for each of the
four steps.

Yaqub Khan

Numerade Educator

Problem 30

A monatomic ideal gas $\left(\gamma=\frac{5}{3}\right)$ is contained within a perfectly insulated cylinder that is fitted with a movable piston. The initial pressure of the gas is $1.50 \times 10^{5}$ Pa. The piston is pushed so as to com- press the gas, with the result that the Kelvin temperature doubles. What is the final pressure of the gas?

Vishal Gupta

Numerade Educator

Problem 31

The pressure and volume of an ideal monatomic gas change from $A$ to $B$ to $C,$ as the drawing shows. The curved line between $A$ and $C$ is an isotherm. (a) Determine the total heat for the process and $(b)$ state whether the flow of heat is into or out of the gas.

Yaqub Khan

Numerade Educator

Problem 32

The work done by one mole of a monatomic ideal gas $\left(\gamma=\frac{5}{3}\right)$ in expanding adiabatically is 825 $\mathrm{J}$ . The initial temperature and volume of the gas are 393 $\mathrm{K}$ and 0.100 $\mathrm{m}^{3} .$ Obtain $\quad$ (a) the final temperature and (b) the final volume of the gas.

Yaqub Khan

Numerade Educator

Problem 33

The drawing shows an adiabatically isolated cylinder that is divided initially into two identical parts by an adiabatic partition. Both sides contain one mole of a monatomic ideal gas $\left(\gamma=\frac{5}{3}\right),$ with the initial temperature being 525 $\mathrm{K}$ on the left and 275 $\mathrm{K}$ on the right. The partition is then allowed to move slowly (i.e., quasi-statically) to the right, until the pressures on each side of the partition are same. Find the final temperatures on the (a) left and (b) right.

Yaqub Khan

Numerade Educator

Problem 34

Argon is a monatomic gas whose atomic mass is 39.9 u. The temperature of eight grams of argon is raised by 75 $\mathrm{K}$ under conditions of constant pressure. Assuming that argon behaves as an ideal gas, how much heat is required?

Yaqub Khan

Numerade Educator

Problem 35

The temperature of 2.5 mol of a monatomic ideal gas is 350 $\mathrm{K}$ . The internal energy of this gas is doubled by the addition of heat. How much heat is needed when it is added at $(\mathrm{a})$ constant volume and $(\mathrm{b})$ constant pressure?

Yaqub Khan

Numerade Educator

Problem 36

Under constant-volume conditions, 3500 $\mathrm{J}$ of heat is added to 1.6 moles of an ideal gas. As a result, the temperature of the gas increases by 75 $\mathrm{K}$ . How much heat would be required to cause the same temperature change under constant-pressure conditions? Do not assume anything
about whether the gas is monatomic, diatomic, etc.

Yaqub Khan

Numerade Educator

Problem 37

Heat is added to two identical samples of a monatomic ideal gas. In the first sample the heat is added while the volume of the gas is kept constant, and the heat causes the temperature to rise by 75 $\mathrm{K}$ . In the second sample, an identical amount of heat is added while the pressure
(but not the volume) of the gas is kept constant. By how much does the temperature of this sample increase?

Yaqub Khan

Numerade Educator

Problem 38

A monatomic ideal gas in a rigid container is heated from 217 $\mathrm{K}$ to 279 $\mathrm{K}$ by adding 8500 $\mathrm{J}$ of heat. How many moles of gas are there in the container?

Yaqub Khan

Numerade Educator

Problem 39

Three moles of a monatomic ideal gas are heated at a constant volume of 1.50 $\mathrm{m}^{3}$ . The amount of heat added is $5.24 \times 10^{3} \mathrm{J}$ . ( a) What is the change in the temperature of the gas? (b) Find the change in its internal energy. (c) Determine the change in pressure.

Narayan Hari

Numerade Educator

Problem 40

A monatomic ideal gas expands at constant pressure. (a) What percentage of the heat being supplied to the gas is used to increase the internal energy of the gas? (b) What percentage is used for doing the work of expansion?

Yaqub Khan

Numerade Educator

Problem 41

Suppose a monatomic ideal gas is contained within a vertical cylinder that is fitted with a movable piston. The piston is frictionless and has a negligible mass. The area of the piston is $3.14 \times 10^{-2} \mathrm{m}^{2},$ and the pressure outside the cylinder is $1.01 \times 10^{5} \mathrm{Pa}$ . Heat $(2093 \mathrm{J})$ is removed from the gas. Through what distance does the piston drop?

Yaqub Khan

Numerade Educator

Problem 42

A monatomic ideal gas is heated while at a constant volume of $1.00 \times 10^{-3} \mathrm{m}^{3},$ using a ten-watt heater. The pressure of the gas increases by $5.0 \times 10^{4}$ Pa. How long was the heater on?

Yaqub Khan

Numerade Educator

Problem 43

One mole of neon, a monatomic gas, starts out at conditions of standard temperature and pressure. The gas is heated at constant volume until its pressure is tripled, then further heated at constant pressure until its volume is doubled. Assume that neon behaves as an ideal gas. For the entire process, find the heat added to the gas.

Yaqub Khan

Numerade Educator

Problem 44

Multiple-Concept Example 6 provides a review of the concepts that play roles here. An engine has an efficiency of 64$\%$ and produces 5500 $\mathrm{J}$ of work. Determine $(\mathrm{a})$ the input heat and $\quad$ (b) the rejected heat.

Yaqub Khan

Numerade Educator

Problem 45

Heat engines take input energy in the form of heat, use some of that energy to do work, and exhaust the remainder. Similarly, a person can be viewed as a heat engine that takes an input of internal energy, uses some of it to do work, and gives off the rest as heat. Suppose that a trained athlete can function as a heat engine with an efficiency of 0.11 . (a) What is the magnitude of the internal energy that the athlete uses in order to do $5.1 \times 10^{4} \mathrm{J}$ of work? (b) Determine the magnitude of the heat the athlete gives off.

Yaqub Khan

Numerade Educator

Problem 46

Engine 1 has an efficiency of 0.18 and requires 5500 J of input heat to perform a certain amount of work. Engine 2 has an efficiency of 0.26 and performs the same amount of work. How much input heat does
the second engine require?

Yaqub Khan

Numerade Educator

Problem 47

Due to a tune-up, the efficiency of an automobile engine increases by 5.0$\%$ . For an input heat of $1300 \mathrm{J},$ how much more work does the engine produce after the tune-up than before?

Yaqub Khan

Numerade Educator

Problem 48

A 52 -kg mountain climber, starting from rest, climbs a vertical distance of 730 $\mathrm{m}$ . At the top, she is again at rest. In the process, her body generates $4.1 \times 10^{6} \mathrm{J}$ of energy via metabolic processes. In fact, her body acts like a heat engine, the efficiency of which is given by Equation 15.11 as $e=|W| / Q_{\mathrm{H}} |,$ where $|W|$ is the magnitude of the work she does and $\left|Q_{\mathrm{H}}\right|$ is the magnitude of the input heat. Find her efficiency as a heat engine.

Yaqub Khan

Numerade Educator

Problem 49

Due to design changes, the efficiency of an engine increases from 0.23 to 0.42. For the same input heat $\left[Q_{\mathrm{H}}, \text { these changes increase }\right.$ the work done by the more efficient engine and reduce the amount of heat rejected to the cold reservoir. Find the ratio of the heat rejected to
the cold reservoir for the improved engine to that for the original engine.

Yaqub Khan

Numerade Educator

Problem 50

Engine A receives three times more input heat, produces five times more work, and rejects two times more heat than engine B. Find the efficiency of $(\mathrm{a})$ engine $\mathrm{A}$ and $\quad(\mathrm{b})$ engine $\mathrm{B}$ .

Surendra Kumar

Numerade Educator

Problem 51

A Carnot engine operates with an efficiency of 27.0$\%$ when the temperature of its cold reservoir is 275 $\mathrm{K}$ . Assuming that the temperature of the hot reservoir remains the same, what must be the temperature of the cold reservoir in order to increase the efficiency to 32.0$\%$ ?

Yaqub Khan

Numerade Educator

Problem 52

An engine has a hot-reservoir temperature of 950 $\mathrm{K}$ and a cold- reservoir temperature of 620 $\mathrm{K}$ . The engine operates at three-fifths maximum efficiency. What is the efficiency of the engine?

Yaqub Khan

Numerade Educator

Problem 53

A Carnot engine has an efficiency of 0.700 , and the temperatureof its cold reservoir is 378 $\mathrm{K}$ . (a) Determine the temperature of its hot reservoir. $(\mathrm{b})$ If 5230 $\mathrm{J}$ of heat is rejected to the cold reservoir, what amount of heat is put into the engine?

Yaqub Khan

Numerade Educator

Problem 54

A Carnot engine operates with a large hot reservoir and a much smaller cold reservoir. As a result, the temperature of the hot reservoir remains constant while the temperature of the cold reservoir slowly increases. This temperature change decreases the efficiency of the engine to 0.70 from $0.75 .$ Find the ratio of the final temperature of the cold reservoir to its initial temperature.

Yaqub Khan

Numerade Educator

Problem 55

An engine does 18500 $\mathrm{J}$ of work and rejects 6550 $\mathrm{J}$ of heat into a cold reservoir whose temperature is 285 $\mathrm{K}$ . What would be the smallest possible temperature of the hot reservoir?

Yaqub Khan

Numerade Educator

Problem 56

A Carnot engine has an efficiency of $0.40 .$ The Kelvin temperature of its hot reservoir is quadrupled, and the Kelvin temperature of its cold reservoir is doubled. What is the efficiency that results from these
changes?

Yaqub Khan

Numerade Educator

Problem 57

A Carnot engine operates between temperatures of 650 and 350 $\mathrm{K}$ . To improve the efficiency of the engine, it is decided either to raise the temperature of the hot reservoir by 40 $\mathrm{K}$ or to lower the temperature of the cold reservoir by 40 $\mathrm{K}$ . Which change gives the greater improvement? Justify your answer by calculating the efficiency in each case.

Yaqub Khan

Numerade Educator

Problem 58

The hot reservoir for a Carnot engine has a temperature of 890 $\mathrm{K}$ while the cold reservoir has a temperature of 670 $\mathrm{K}$ . The heat input for this engine is 4800 $\mathrm{J}$ . The $670-\mathrm{K}$ reservoir also serves as the hot reservoir for a second Carnot engine. This second engine uses the rejected heat of the first engine as input and extracts additional work from it. The rejected heat from the second engine goes into a reservoir that has a temperature of 420 $\mathrm{K}$ . Find the total work delivered by thetwo engines.

Yaqub Khan

Numerade Educator

Problem 59

Suppose that the gasoline in a car engine burns at $631^{\circ} \mathrm{C}$ , while the exhaust temperature (the temperature of the cold reservoir) is $139^{\circ} \mathrm{C}$ and the outdoor temperature is $27^{\circ} \mathrm{C}$ . Assume that the engine can be treated as a Carnot engine (a gross oversimplification). In an attempt to increase mileage performance, an inventor builds a second engine that functions between the exhaust and outdoor temperatures and uses the exhaust heat to produce additional work. Assume that the inventor's engine can also be treated as a Carnot engine. Determine the ratio of the total work produced by both engines to that produced by the first engine alone.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 60

A power plant taps steam superheated by geothermal energy to 505 $\mathrm{K}$ (the temperature of the hot reservoir) and uses the steam to do work in turning the turbine of an electric generator. The steam is then converted back into water in a condenser at 323 $\mathrm{K}$ (the temperature of the cold reservoir), after which the water is pumped back down into the earth where it is heated again. The output power (work per unit time) of the plant is 84000 kilowatts. Determine (a) the maximum efficiency at which this plant can operate and $(\mathbf{b})$ the minimum amount of rejected heat that must be removed from the condenser every twenty-four hours.

Yaqub Khan

Numerade Educator

Problem 61

The drawing (not to scale) shows the way in which the pressure and volume change for an ideal gas that is used as the working substance in a Carnot engine. The gas begins at point a (pressure $=P_{a},$
volume $=V_{\mathrm{a}}$ and expands isothermally at temperature $T_{\mathrm{H}}$ until point b
(pressure $=P_{\mathrm{b}}$ , volume $=V_{\mathrm{b}}$ is reached. During this expansion, the input heat of magnitude $\left|Q_{\mathrm{H}}\right|$ enters the gas from the hot reservoir of the engine. Then, from point b to point $c$ (pressure $=P_{c},$ volume $=V_{c} )$ the gas expands adiabatically. Next, the gas is compressed isothermally at temperature $T_{\mathrm{C}}$ from point $c$ to point $\mathrm{d}$ (pressure $=P_{\mathrm{d}},$ volume $=V_{\mathrm{d}} )$ During this compression, heat of magnitude $\left|Q_{\mathrm{C}}\right|$ is rejected to the cold reservoir of the engine. Finally, the gas is compressed adiabatically from point d to point a, where the gas is back in its initial state. The overall process a to b to c to d to a is called a Carnot cycle. Prove for this cycle
that $\left|Q_{\mathrm{c}}\right| /\left|Q_{\mathrm{H}}\right|=T_{\mathrm{C}} / T_{\mathrm{H}} .$

Yaqub Khan

Numerade Educator

Problem 62

A nuclear-fueled electric power plant utilizes a so-called boiling water reactor In this type of reactor, nuclear energy causes water underpressure to boil at $285^{\circ} \mathrm{C}$ the temperature of the hot reservoir). After the steam does the work of turning the turbine of an electric generator, the steam is converted back into water in a condenser at $40^{\circ} \mathrm{C}$ (the temperature of the cold reservoir). To keep the condenser at $40^{\circ} \mathrm{C},$ the rejected heat must be carried away by some means-for example, by water from a river. The plant operates at three-fourths of its Carnot efficiency, and the water flow rate of $1.0 \times 10^{5} \mathrm{kg} / \mathrm{s}$ is available to remove the rejected heat from the plant. Find the number of Celsius degrees by which the temperature of the river rises.

Yaqub Khan

Numerade Educator

Problem 63

A Carnot air conditioner maintains the temperature in a house at 297 $\mathrm{K}$ on a day when the temperature outside is 311 $\mathrm{K}$ . What is the coefficient of performance of the air conditioner?

Yaqub Khan

Numerade Educator

Problem 64

The inside of a Carnot refrigerator is maintained at a temperature of 277 $\mathrm{K}$ , while the temperature in the kitchen is 299 $\mathrm{K}$ . Using 2500 $\mathrm{J}$ of work, how much heat can this refrigerator remove from its inside compartment?

Yaqub Khan

Numerade Educator

Problem 65

A refrigerator operates between temperatures of 296 and 275 $\mathrm{K}$ . What would be its maximum coefficient of performance?

Yaqub Khan

Numerade Educator

Problem 66

Two Carnot air conditioners, $A$ and $B,$ are removing heat from different rooms. The outside temperature is the same for both rooms, 309.0 $\mathrm{K}$ . The room serviced by unit A is kept at a temperature of 294.0 $\mathrm{K}$ , while the room serviced by unit $\mathrm{B}$ is kept at 301.0 $\mathrm{K}$ . The heat removed from either room is 4330 $\mathrm{J}$ J. For both units, find the magnitude of the work required and the magnitude of the heat deposited outside.

Yaqub Khan

Numerade Educator

Problem 67

See Multiple-Concept Example 10 to review the concepts that are important in this problem. The water in a deep underground well is used as the cold reservoir of a Carnot heat pump that maintains the temperature of a house at 301 $\mathrm{K}$ . To deposit 14200 $\mathrm{J}$ of heat in the house, the heat pump requires 800 $\mathrm{J}$ of work. Determine the temperature of the well water.

Yaqub Khan

Numerade Educator

Problem 68

A Carnot engine has an efficiency of $0.55 .$ If this engine were run backward as a heat pump, what would be the coefficient of performance?

Yaqub Khan

Numerade Educator

Problem 69

A Carnot refrigerator is used in a kitchen in which the temperature is kept at 301 $\mathrm{K}$ . This refrigerator uses 241 $\mathrm{J}$ of work to remove 2561 $\mathrm{J}$ of heat from the food inside. What is the temperature inside the refrigerator?

Yaqub Khan

Numerade Educator

Problem 70

The wattage of a commercial ice maker is 225 $\mathrm{W}$ and is the rate at which it does work. The ice maker operates just like a refrigerator or an air conditioner and has a coefficient of performance of $3.60 .$ The water going into the unit has a temperature of $15.0^{\circ} \mathrm{C},$ and the ice maker produces ice cubes at $0.0^{\circ} \mathrm{C}$ . Ignoring the work needed to keep stored ice from melting, find the maximum amount (in $\mathrm{kg}$ ) of ice that the unit can produce in one day of continuous operation.

Yaqub Khan

Numerade Educator

Problem 71

Review Conceptual Example 9 before attempting this problem. A window air conditioner has an average coefficient of performance of $2.0 .$ In a futile attempt to cool a bedroom, this unit has been placed on the floor by the bed. During this attempt, $7.6 \times 10^{4} \mathrm{J}$ of heat is removed from the air in the front of the unit. Determine the net heat added to the room by operating the air conditioner in this manner.

Yaqub Khan

Numerade Educator

Problem 72

How long would a $3.00-\mathrm{kW}$ space have to run to put into a kitchen the same amount of heat as a refrigerator (coefficient of performance $=3.00$ ) does when it freezes 1.50 $\mathrm{kg}$ of water at $20.0^{\circ} \mathrm{C}$ into ice at $0.0^{\circ} \mathrm{C} ?$

Yaqub Khan

Numerade Educator

Problem 73

A Carnot refrigerator transfers heat from its inside $\left(6.0^{\circ} \mathrm{C}\right)$ to the room air outside $\left(20.0^{\circ} \mathrm{C}\right)$ . (a) Find the coefficient of performance of the refrigerator. $(\mathbf{b})$ Determine the magnitude of the minimum work needed to cool 5.00 $\mathrm{kg}$ of water from 20.0 to $6.0^{\circ} \mathrm{C}$ when it is placed in the refrigerator.

Yaqub Khan

Numerade Educator

Problem 74

A Carnot engine uses hot and cold reservoirs that have temperatures of 1684 and 842 $\mathrm{K}$ , respectively. The input heat for this engine is $\left|Q_{\mathrm{H}}\right|$ The work delivered by the engine is used to operate a Carnot heat pump. The pump removes heat from the $842-\mathrm{K}$ reservoir and puts it into a hot reservoir at a temperature $T^{\prime}$ . The amount of heat removed from the $842-\mathrm{K}$ reservoir is also $\left|Q_{\mathrm{H}}\right| .$ Find the temperature $T^{\prime}$

Yaqub Khan

Numerade Educator

Problem 75

Consider three engines that each use 1650 $\mathrm{J}$ of heat from a hot reservoir (temperature $=550 \mathrm{K} ) .$ These three engines reject heat to a cold reservoir (temperature $=330 \mathrm{K} ) .$ Engine I rejects 1120 $\mathrm{J}$ of heat. Engine II rejects 990 $\mathrm{J}$ of heat. Engine III rejects 660 $\mathrm{J}$ of heat. One of the two irreversible engines, one violates the second law of thermodynamics and could not exist. For each of the engines determine the total entropy change of the universe, which is the sum of the entropy changes of the hot and cold reservoirs. On the basis of your calculations, identify which engine operates reversibly, which operates irreversibly and could exist,
and which operates irreversibly and could not exist.

Yaqub Khan

Numerade Educator

Problem 76

Heat $Q$ flows spontaneously from a reservoir at 394 $\mathrm{K}$ into a reservoir at 298 $\mathrm{K}$ . Because of the spontaneous flow, 2800 $\mathrm{J}$ of energy is rendered unavailable for work when a Carnot engine operates between the reservoir at 298 $\mathrm{K}$ and a reservoir at 248 $\mathrm{K}$ . Find $Q$ .

Vipender Yadav

Numerade Educator

Problem 77

Find the change in entropy of the $\mathrm{H}_{2} \mathrm{O}$ molecules when (a) three kilograms of ice melts into water at 273 $\mathrm{K}$ and $(\mathrm{b})$ three kilograms of water changes into steam at 373 $\mathrm{K}$ . (c) On the basis of the answers to parts (a) and (b), discuss which change creates more disorder in the collection of $\mathrm{H}_{2} \mathrm{O}$ molecules.

Yaqub Khan

Numerade Educator

Problem 78

On a cold day, 24500 $\mathrm{J}$ of heat leaks out of a house. The inside temperature is $21^{\circ} \mathrm{C},$ and the outside temperature is $-15^{\circ} \mathrm{C}$ . What is the increase in the entropy of the universe that this heat loss produces?

Yaqub Khan

Numerade Educator

Problem 79

(a) After 6.00 $\mathrm{kg}$ of water at $85.0^{\circ} \mathrm{C}$ is mixed in a perfect thermos with 3.00 $\mathrm{kg}$ of ice at $0.0^{\circ} \mathrm{C},$ the mixture is allowed to reach equilibrium. When heat is added to or removed from a solid or liquid of mass $m$ and specific heat capacity $c$ , the change in entropy can be shown to be $\Delta S=m c \ln \left(T_{\mathrm{f}} / T_{\mathrm{i}}\right),$ where $T_{\mathrm{i}}$ and $T_{\mathrm{f}}$ are the initial and final Kelvin temperatures. Using this expression and the change in entropy for melting, find the change in entropy that occurs. $(\mathrm{b})$ Should the entropy of the universe increase or decrease as a result of the mixing process? Give your reasoning and state whether your answer in part (a) is consistent with your answer here.

Yaqub Khan

Numerade Educator

Problem 80

The sun is a sphere with a radius of $6.96 \times 10^{8} \mathrm{m}$ and an average surface temperature of 5800 k. Determine the amount by which the sun's thermal radiation increases the entropy of the entire universe each second. Assume that the sun is a perfect blackbody, and that the average
temperature of the rest of the universe is 2.73 $\mathrm{K}$ . Do not consider the thermal radiation absorbed by the sun from the rest of the universe.

Yaqub Khan

Numerade Educator

Problem 81

An irreversible engine operates between temperatures of 852 and 314 $\mathrm{K}$ . It absorbs 1285 $\mathrm{J}$ of heat from the hot reservoir and does 264 $\mathrm{J}$ of work. $\quad$ (a) What is the change $\Delta S_{\text { universe }}$ in the entropy of the universe associated with the operation of this engine? $(\mathbf{b})$ If the engine were reversible, what would be the magnitude $|W|$ of the work it would have done, assuming that it operated between the same temperatures and absorbed the same heat as the irreversible engine? (c) Using the results of parts (a) and (b), find the difference between the work produced by the reversible and irreversible engines.

Yaqub Khan

Numerade Educator

Problem 82

The pressure of a monatomic ideal gas $\left(\gamma=\frac{5}{3}\right)$ doubles during an
adiabatic compression. What is the ratio of the final volume to the initial volume?

Yaqub Khan

Numerade Educator

Problem 83

One-half mole of a monatomic ideal gas absorbs 1200 $\mathrm{J}$ of heat while 2500 $\mathrm{J}$ of work is done by the gas. (a) What is the temperature change of the gas? (b) Is the change an increase or a decrease?

Yaqub Khan

Numerade Educator

Problem 84

Multiple-Concept Example 6 deals with the same concepts as this problem does. What is the efficiency of a heat engine that uses an input heat of $5.6 \times 10^{4} \mathrm{J}$ and rejects $1.8 \times 10^{4} \mathrm{J}$ of heat?

Yaqub Khan

Numerade Educator

Problem 85

A gas, while expanding under isobaric conditions, does 480 $\mathrm{J}$ of work. The pressure of the gas is $1.6 \times 10^{5} \mathrm{Pa}$ , and its initial volume is $1.5 \times 10^{-3} \mathrm{m}^{3} .$ What is the final volume of the gas?

Yaqub Khan

Numerade Educator

Problem 86

A lawnmower engine with an efficiency of 0.22 rejects 9900 $\mathrm{J}$ of heat every second. What is the magnitude of the work that the engine does in one second?

Yaqub Khan

Numerade Educator

Problem 87

A process occurs in which the entropy of a system increases by 125 $\mathrm{J} / \mathrm{K}$ . During the process, the energy that becomes unavailable for doing work is zero. $\quad$ (a) Is process reversible or irreversible? Give your reasoning. (b) Determine the change in the entropy of the surroundings.

Yaqub Khan

Numerade Educator

Problem 88

A Carnot heat pump operates between an outdoor temperature of 265 $\mathrm{K}$ and an indoor temperature of 298 $\mathrm{K}$ . Find its coefficient of performance.

Yaqub Khan

Numerade Educator

Problem 89

The temperatures indoors and outdoors are 299 and $312 \mathrm{K},$ respectively. A Carnot air conditioner deposits $6.12 \times 10^{5} \mathrm{J}$ of heat outdoors. How much heat is removed from the house?

Yaqub Khan

Numerade Educator

Problem 90

Carnot engine $\mathrm{A}$ has an efficiency of $0.60,$ and Carnot engine $\mathrm{B}$
has an efficiency of $0.80 .$ Both engines utilize the same hot reservoir, which has a temperature of 650 $\mathrm{K}$ and delivers 1200 $\mathrm{J}$ of heat to each engine. Find the magnitude of the work produced by each engine and the temperatures of the cold reservoirs that they use.

Yaqub Khan

Numerade Educator

Problem 91

The pressure and volume of a gas are changed along the path $A B C A$ . Using the data
shown in the graph, determine the work done (including the algebraic sign) in each segment
of the path: (a) $A$ to $B,$ (b) $B$ to $C,$ and $\quad$ (c) $C$ to $A$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 92

Refer to the drawing in Problem $12,$ where the curve between $A$ and $B$ is now an
isotherm. An ideal gas begins at $A$ and is changed along the horizontal line from $A$ to $C$ and
then along the vertical line from $C$ to $B$ . (a) Find the heat for the process $A C B$ and $\quad(b)$ determine whether it flows into or out of the gas.

Yaqub Khan

Numerade Educator

Problem 93

Suppose that 31.4 $\mathrm{J}$ of heat is added to an ideal gas. The gas expands at a constant pressure of $1.40 \times 10^{4}$ Pa while changing its volume from $3.00 \times 10^{-4}$ to $8.00 \times 10^{-4} \mathrm{m}^{3}$ . The gas is not monatomic, so the relation $C_{P}=\frac{5}{2} R$ does not apply. (a) Determine the change in the internal energy of the gas. (b) Calculate its molar specific heat
capacity $C_{p} .$

Yaqub Khan

Numerade Educator

Problem 94

An air conditioner keeps the inside of a house at a temperature of $19.0^{\circ} \mathrm{C}$ when the outdoor temperature is $33.0^{\circ} \mathrm{C} .$ Heat, leaking into the house at the rate of 10500 joules per second, is removed by the air conditioner. Assuming that the air conditioner is a Carnot air conditioner, what is the work per second that must be done by the electrical energy in order to keep the inside temperature constant?

Yaqub Khan

Numerade Educator

Problem 95

Even at rest, the human body generates heat. The heat arises because of the body's metabolism- that is, the chemical reactions that are always occurring in the body to generate energy. In rooms designed for use by large groups, adequate ventilation or aissroom conditioning must be provided to remove this heat. Consider a classroom containing 200 students. Assume that the metabolic rate of generating heat is 130 $\mathrm{W}$ for each student and that the heat accumulates during a fifty-minute lecture. In addition, assume that the air has a molar specific heat of $C_{V}=\frac{5}{2} R$ and that the room (volume $=1200 \mathrm{m}^{3},$ initial pressure $=$ $1.01 \times 10^{5} \mathrm{Pa}$ and initial temperature $=21^{\circ} \mathrm{C}$ ) is sealed shut. If all the heat generated by the students were absorbed by the air, by how much would the air temperature rise during a lecture?

Yaqub Khan

Numerade Educator

Problem 96

Heat flows from a reservoir at 373 $\mathrm{K}$ to a reservoir at 273 $\mathrm{K}$ through a $0.35-\mathrm{m}$ copper rod with a cross-sectional area of $9.4 \times 10^{-4} \mathrm{m}^{2}$ (see the drawing). The heat then leaves the $273-\mathrm{K}$ reservoir and enters a Carnot engine, which uses part of this heat to do work and rejects the remainder to a third reservoir at 173 $\mathrm{K}$ . How much of the heat leaving the $373-\mathrm{K}$ reservoir is rendered unavailable for doing work in a period of 2.0 $\mathrm{min} ?$

Yaqub Khan

Numerade Educator

Problem 97

A fifteen-watt heater is used to heat a monatomic ideal gas at a constant pressure of
$7.60 \times 10^{5}$ Pa. During the process, the $1.40 \times 10^{-3} \mathrm{m}^{3}$ volume of the
gas increases by 25.0$\% .$ How long was the heater on?

Yaqub Khan

Numerade Educator

Problem 98

An ideal gas is taken through the three processes $(\mathrm{A} \rightarrow \mathrm{B}, \quad \mathrm{B} \rightarrow \mathrm{C}, \text { and } \mathrm{C} \rightarrow \mathrm{A})$
shown in the drawing. In general, for each process the internal energy $U$ of the gas can change
because heat $Q$ can be added to or removed from the gas and work $W$ can be done by the gas or on the gas. For the three processes shown in the drawing, fill in the five missing entries in the following table.

Supratim Pal

Numerade Educator

Problem 99

An engine has an efficiency $e_{1} .$ The engine takes input heat of magnitude $\left|Q_{\mathrm{H}}\right|$ from a hot reservoir and delivers work of magnitude $\left|W_{1}\right|$ The heat rejected by this engine is used as input heat for a second engine, which has an efficiency $e_{2}$ and delivers work of magnitude $\left|W_{2}\right| .$ The overall efficiency of this two-engine device is the magnitude of the total work delivered $\left(\left|W_{1}\right|+\left|W_{2}\right|\right)$ divided by the magnitude $\left|Q_{\mathrm{H}}\right|$ of the input heat. Find an expression for the overall efficiency $e$ in terms of $e_{1}$ and $e_{2}$

Yaqub Khan

Numerade Educator

Problem 100

Beginning with a pressure of $2.20 \times 10^{5}$ Pa and a volume of $6.34 \times 10^{-3} \mathrm{m}^{3},$ an ideal monatomic gas $\left(\gamma=\frac{5}{3}\right)$ undergoes an adiabatic
expansion such that its final pressure is $8.15 \times 10^{4} \mathrm{Pa}$ . An alternatice process leading to the same final state begins with an isochoric cooling to the final pressure, followed by an isobaric expansion to the final volume. How much more work does the gas do in the adiabatic process
than in the alternative process?

Yaqub Khan

Numerade Educator