Deck 15: The Laws of Thermodynamics

Question 1

Choose the one alternative that best completes the statement or answers the question.
A cyclic process is carried out on an ideal gas such that it returns to its initial state at the end of a cycle, as shown in the $p V$ diagram in the figure. If the process is carried out in a counter-clockwise sense around the enclosed area, as shown on the figure, then the magnitude of the enclosed area represents

A) the work done by the gas.
B) the work done on the gas.
C) the heat added to the gas.
D) the heat that flows out of the gas.

Answer 1

B

Question 2

Choose the one alternative that best completes the statement or answers the question.
A Carnot cycle consists of

A) four isotherms.
B) two adiabats and two isotherms.
C) four adiabats.
D) two adiabats and two isobars.
E) two isobars and two isotherms.

Answer 2

B

Question 3

Choose the one alternative that best completes the statement or answers the question.
The figure shows a $p V$ diagram for $0.98$ mol of ideal gas that undergoes the process $1 \rightarrow 2$ . The gas then undergoes an isochoric heating from point 2 until the pressure is restored to the value it had at point 1. What is the final temperature of the gas? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$ .

A) $380 ^ { \circ } \mathrm { C }$
B) $110 ^ { \circ } \mathrm { C }$
C) $- 160 ^ { \circ } \mathrm { C }$
D) $12 ^ { \circ } \mathrm { C }$

Answer 3

C

Question 4

Choose the one alternative that best completes the statement or answers the question.
A gas is taken through the cycle shown in the $p V$ diagram in the figure. During one cycle, how much work is done by the gas?

A) $2 p _ { 0 } V _ { 0 }$
B) $3 p _ { 0 } V _ { 0 }$
C) $p _ { 0 } V _ { 0 }$
D) $4 p _ { 0 } V _ { 0 }$

Question 5

Choose the one alternative that best completes the statement or answers the question.
A cyclic process is carried out on an ideal gas such that it returns to its initial state at the end of a cycle, as shown in the $p V$ diagram in the figure. If the process is carried out in a clockwise sense around the enclosed area, as shown on the figure, then the magnitude of the enclosed area represents

A) the heat added to the gas.
B) the work done by the gas.
C) the heat that flows out of the gas.
D) the work done on the gas.

Question 6

Choose the one alternative that best completes the statement or answers the question.
A certain gas is compressed adiabatically. The amount of work done on the gas is $800 \mathrm {~J}$ . What is the change in the internal (thermal) energy of the gas?

A) $800 \mathrm {~J}$
B) $0 \mathrm {~J}$
C) $- 800 \mathrm {~J}$
D) $400 \mathrm {~J}$
E) More information is needed to answer this question.

Question 7

Choose the one alternative that best completes the statement or answers the question.
The figure shows a $p V$ diagram for $0.0077$ mol of ideal gas that undergoes the process $1 \rightarrow 2 \rightarrow 3$ . What is the volume $V _ { 3 }$ ? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$
$p$ (atm)

A) $0 \mathrm {~cm} ^ { 3 }$
B) $770 \mathrm {~cm} ^ { 3 }$
C) $400 \mathrm {~cm} ^ { 3 }$
D) $0 \mathrm {~cm} ^ { 3 }$

Question 8

Choose the one alternative that best completes the statement or answers the question.
The figure shows a $p V$ diagram for $2.6 \mathrm {~g}$ of ideal helium gas that undergoes the process $1 \rightarrow 2 \rightarrow 3$ . Find the value of volume $V _ { 3 }$ . The atomic mass of helium is $4.0 \mathrm {~g} / \mathrm { mol }$ , and $R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K }$ .

A) $50 \mathrm {~L}$
B) $99 \mathrm {~L}$
C) $25 \mathrm {~L}$
D) $12 \mathrm {~L}$

Question 9

Choose the one alternative that best completes the statement or answers the question.
The process shown on the $p V$ diagram in the figure is

A) isobaric.
B) isochoric.
C) isothermal.
D) adiabatic.

Question 10

Choose the one alternative that best completes the statement or answers the question.
Which of the following is a false statement?

A) The total entropy change in one cycle of a Carnot engine is zero.
B) Entropy is a quantitative measure of disorder.
C) The entropy of an isolated system must be conserved (it remains constant).
D) Entropy can be measured in units of $\mathrm { J } / \mathrm { K }$ .

Question 11

Choose the one alternative that best completes the statement or answers the question.
The figure shows a $p V$ diagram for $8.3 \mathrm {~g}$ of ideal nitrogen gas $\mathrm { N } _ { 2 }$ in a sealed container. The temperature of state 1 is $59 ^ { \circ } \mathrm { C }$ , the atomic mass of the nitrogen atom is $14 \mathrm {~g} / \mathrm { mol }$ , and $R = 8.31 \mathrm {~J} / \mathrm { mol }$ - K. What are (a) pressure $p _ { 1 }$ and (b) temperature $T _ { 2 }$ ?

A) (a) $81 \mathrm {~atm}$ , (b) $120 ^ { \circ } \mathrm { C }$
B) (a) 81 atm, (b) $660 ^ { \circ } \mathrm { C }$
C) (a) $14 \mathrm {~atm}$ , (b) $120 ^ { \circ } \mathrm { C }$
D) (a) $14 \mathrm {~atm}$ , (b) $660 ^ { \circ } \mathrm { C }$

Question 12

Choose the one alternative that best completes the statement or answers the question.
When water at $0 ^ { \circ } \mathrm { C }$ freezes, the entropy of the water

A) increases.
B) remains constant.
C) decreases.
D) could either increase or decrease; it depends on other factors.

Question 13

Choose the one alternative that best completes the statement or answers the question.
The temperature of an ideal gas in a sealed rigid $0.20 - \mathrm { m } ^ { 3 }$ container is reduced from $360 \mathrm {~K}$ to $270 \mathrm {~K}$ , and the final pressure of the gas is 40 kPA. How much work is done by the gas during this process? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

A) $- 12 \mathrm {~kJ}$
B) $9.0 \mathrm {~kJ}$
C) $0 \mathrm {~kJ}$
D) $- 9.0 \mathrm {~kJ}$
E) $12 \mathrm {~kJ}$

Question 14

Choose the one alternative that best completes the statement or answers the question.
An ideal gas undergoes an isothermal expansion. During this process, its entropy

A) increases.
B) decreases.
C) remains unchanged.
D) cannot be predicted from the data given.

Question 15

Choose the one alternative that best completes the statement or answers the question.
The process shown on the $p V$ diagram in the figure is an

A) isometric expansion.
B) isothermal expansion.
C) adiabatic expansion.
D) isobaric expansion.

Question 16

Choose the one alternative that best completes the statement or answers the question.
The figure shows a $p V$ diagram for $0.0061$ mol of ideal gas that undergoes the process $1 \rightarrow 2 \rightarrow 3$ . What is the pressure $p _ { 2 } ? ( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$
$p$ (atm)

A) $15 \mathrm {~atm}$
B) $1.5 \times 10 ^ { 6 } \mathrm {~atm}$
C) $4.9 \times 10 ^ { 5 } \mathrm {~atm}$
D) $4.9 \mathrm {~atm}$

Question 17

Choose the one alternative that best completes the statement or answers the question.
The figure shows a $p V$ diagram for $2.9 \mathrm {~g}$ of ideal oxygen gas $\mathrm { O } _ { 2 }$ in a sealed container. The temperature of state 1 is $76 ^ { \circ } \mathrm { C }$ , the atomic mass of the oxygen atom is $16 \mathrm {~g} / \mathrm { mol }$ , and $R = 8.31 \mathrm {~J} / \mathrm { mol }$ -K. What are the temperatures $T _ { 3 }$ and $T _ { 4 }$ ?

A) $260 ^ { \circ } \mathrm { C }$ and $790 ^ { \circ } \mathrm { C }$
B) $- 11 ^ { \circ } \mathrm { C }$ and $510 ^ { \circ } \mathrm { C }$
C) $38 ^ { \circ } \mathrm { C }$ and $110 ^ { \circ } \mathrm { C }$
D) $57 ^ { \circ } \mathrm { C }$ and $170 ^ { \circ } \mathrm { C }$

Question 18

Choose the one alternative that best completes the statement or answers the question.
If the efficiency of a Carnot engine were to be $100 \%$ , the heat sink would have to be

A) at $100 ^ { \circ } \mathrm { C }$ .
B) at $0 ^ { \circ } \mathrm { C }$ .
C) infinitely hot.
D) at absolute zero.

Question 19

Choose the one alternative that best completes the statement or answers the question.
Two processes are shown on the $p V$ diagram in the figure. One of them is an adiabat and the other one is an isotherm. Which process is the isotherm?

A) process $A$
B) process $B$
C) The processes shown are neither isotherms nor adiabats.
D) It is not possible to tell without knowing if the gas is monatomic or diatomic.

Question 20

Choose the one alternative that best completes the statement or answers the question.
A 10-L flask and a 1-L flask each contain two moles of ideal diatomic gas (but not the same gas) at $25 ^ { \circ } \mathrm { C }$ . Which of the following statements about these gases must be true? (There could be more than one correct choice.)

A) The internal (thermal) energy of the gas in the smaller flask is greater than the internal (thermal) energy of the gas in the larger flask.
B) The molecules in the larger flask have the same root-mean-square speed as those in the smaller flask.
C) The internal (thermal) energy of the gas in the larger flask is greater than the internal (thermal) energy of the gas in the smaller flask.
D) The molecules in the smaller flask have the same average kinetic energy per molecule as those in the larger flask.
E) The internal (thermal) energy of the gas in both flasks is the same.

Question 21

Write the word or phrase that best completes each statement or answers the question.
The figure shows a $p V$ diagram for a gas going through a cycle from $A$ to $B$ to $C$ and back to A. From point $A$ to point $B$ , the gas absorbs $50 \mathrm {~J}$ of heat and finds its internal (thermal) energy has increased by $20 \mathrm {~J}$ . Going from B to $C$ , the internal (thermal) energy decreases by $5.0 \mathrm {~J}$ .
(a) How much work was done by the gas from $A$ to $B$ ?
(b) How much heat was absorbed by the gas from $B$ to $C$ ?
(c) How much work was done by the gas going from $B$ to $C$ ?

Question 22

Choose the one alternative that best completes the statement or answers the question.
A gas expands from an initial volume of $0.040 \mathrm {~m} ^ { 3 }$ to a final volume of $0.085 \mathrm {~m} ^ { 3 }$ while its pressure increases linearly with the volume (so that the process follows a straight-line path in a $p V$ diagram) from $110 \mathrm { kPa }$ to $225 \mathrm { kPa }$ . How much work is done by the gas during this expansion?

A) $11 \mathrm {~kJ}$
B) $7.8 \mathrm {~kJ}$
C) $12 \mathrm {~kJ}$
D) $5.2 \mathrm {~kJ}$
E) $7.5 \mathrm {~kJ}$

Question 23

Write the word or phrase that best completes each statement or answers the question.
An ideal gas undergoes the process $a \rightarrow b \rightarrow c \rightarrow a$ shown in the $p V$ diagram. The heat gained by the gas in process $a \rightarrow b$ is $546 \mathrm {~J}$ , while in process $b \rightarrow c$ the gas loses $62.0 \mathrm {~J}$ of heat. In process $a \rightarrow b$ the gas performs $310 \mathrm {~J}$ of work, while in process $c \rightarrow a 223 \mathrm {~J}$ of work is done on the gas. How much heat is gained by the gas in process $c \rightarrow a$ ?

A) $- 236 \mathrm {~J}$
B) $- 62 \mathrm {~J}$
C) $18 \mathrm {~J}$
D) $- 397 \mathrm {~J}$
E) $223 \mathrm {~J}$

Question 24

Write the word or phrase that best completes each statement or answers the question.
A certain automobile engine takes in 4.00 kJ of heat and performs 1.10 kJ of mechanical
work in each cycle.
(a) Calculate the engine's efficiency.
(b) How much heat is "wasted" in each cycle?

Question 25

Choose the one alternative that best completes the statement or answers the question.
An ideal gas undergoes the process $a \rightarrow b \rightarrow c \rightarrow a$ shown in the $p V$ diagram. In this figure, $P _ { a } = P _ { c } =$ $3.60 \times 10 ^ { 5 } \mathrm {~Pa} , V _ { b } = V _ { c } = 68.00 \mathrm {~L} , V _ { a } = 35 \mathrm {~L}$ , and $P _ { b } = 5.60 \times 10 ^ { 5 } \mathrm {~Pa}$ . How much work is done by the system in this process?

A) $3300 \mathrm {~J}$
B) $2800 \mathrm {~J}$
C) $3000 \mathrm {~J}$
D) $2300 \mathrm {~J}$
E) $3800 \mathrm {~J}$

Question 26

Choose the one alternative that best completes the statement or answers the question.
The figure shows a $p V$ diagram for an ideal gas that is carried around a cyclic process. How much work is done in one cycle if $p _ { 0 } = 4.00 \mathrm {~atm}$ and $\mathrm { V } _ { 0 } = 3.00 \mathrm {~L}$ ? $( 1.00 \mathrm {~atm} = 101 \mathrm { kPa } )$

A) $1210 \mathrm {~J}$
B) $485 \mathrm {~J}$
C) $2420 \mathrm {~J}$
D) $2280 \mathrm {~J}$
E) $4850 \mathrm {~J}$

Question 27

Write the word or phrase that best completes each statement or answers the question.
During each cycle, a heat engine takes in 4.0 J of heat, does 1.0 J of work, and expels 3.0 J
of heat. What is its efficiency?

Question 28

Write the word or phrase that best completes each statement or answers the question.
A 40.0-L container is divided into two equal parts by a rubber membrane. One half of the container has $1.50$ moles of an ideal monatomic gas at $250 \mathrm {~K}$ , and the other half is a vacuum. The container is well insulated, so there is no exchange of heat with the surroundings. The membrane breaks, and eventually the gas reaches a new equilibrium condition occupying the entire volume. What is the final temperature of the gas?

A) $125 \mathrm {~K}$
B) $100 \mathrm {~K}$
C) $157 \mathrm {~K}$
D) $180 \mathrm {~K}$
E) $250 \mathrm {~K}$

Question 29

Write the word or phrase that best completes each statement or answers the question.
A heat engine absorbs 64 kcal of heat each cycle and exhausts 42 kcal.
(a) What is the efficiency of this engine?
(b) How much work does this engine do per cycle?

Question 30

Write the word or phrase that best completes each statement or answers the question.
The figure shows a $p V$ diagram of a gas for a complete cycle. During part $b c$ of the cycle, $1190 \mathrm {~J}$ of heat flows into a system, and at the same time the system expands against a constant external pressure of $7.00 \times 10 ^ { 4 } \mathrm {~Pa}$ as its volume increases from $0.0200 \mathrm {~m} ^ { 3 }$ to $0.0800 \mathrm {~m} ^ { 3 }$ . Calculate the change in internal (thermal) energy of the system during part $b c$ of the cycle. If the change is nonzero, be sure to indicate whether the change is positive or negative.

Question 31

Write the word or phrase that best completes each statement or answers the question.
An ideal gas undergoes the process $a \rightarrow b \rightarrow c \rightarrow a$ shown in the $p V$ diagram. In the figure, $P _ { a } = P _ { C } =$ $240 \mathrm { kPa } , V _ { b } = V _ { c } = 40 \mathrm {~L} , V _ { a } = 15 \mathrm {~L}$ , and $P _ { b } = 400 \mathrm { kPa }$ . How much heat is gained by the gas in this $a$ $\rightarrow b \rightarrow c \rightarrow a$ process?

A) $1500 \mathrm {~J}$
B) $2500 \mathrm {~J}$
C) $1000 \mathrm {~J}$
D) $2000 \mathrm {~J}$
E) $3000 \mathrm {~J}$

Question 32

Choose the one alternative that best completes the statement or answers the question.
During an isothermal process, $5.0 \mathrm {~J}$ of heat is removed from an ideal gas. What is the change in internal (thermal) energy of the gas?

A) $10 \mathrm {~J}$
B) $2.5 \mathrm {~J}$
C) $5.0 \mathrm {~J}$
D) $0 \mathrm {~J}$

Question 33

Write the word or phrase that best completes each statement or answers the question.
A heat engine has an efficiency of 35.0% and receives 150 J of heat per cycle.
(a) How much work does it do in each cycle?
(b) How much heat does it "waste" in each cycle?

Question 34

Choose the one alternative that best completes the statement or answers the question.
A compression at a constant pressure of $200 \mathrm { kPa }$ is performed on $8.00$ moles of an ideal monatomic gas. The compression reduces the volume of the gas from $0.200 \mathrm {~m} ^ { 3 }$ to $0.120 \mathrm {~m} ^ { 3 }$ . How much work was done by the gas during this process?

A) $- 40 \mathrm {~kJ}$
B) $0 \mathrm {~kJ}$
C) $40 \mathrm {~kJ}$
D) $16 \mathrm {~kJ}$
E) $- 16 \mathrm {~kJ}$

Question 35

Write the word or phrase that best completes each statement or answers the question.
A heat engine with an efficiency of $30 \%$ performs $2500 \mathrm {~J}$ of work. How much heat is discharged to the lower temperature reservoir?

A) $1400 \mathrm {~J}$
B) $8300 \mathrm {~J}$
C) $7100 \mathrm {~J}$
D) $5800 \mathrm {~J}$
E) $750 \mathrm {~J}$

Question 36

Choose the one alternative that best completes the statement or answers the question.
A gas expands from an initial volume of $30.0 \mathrm {~L}$ to a final volume of $65.0 \mathrm {~L}$ at a constant pressure of $110 \mathrm { kPa }$ . How much work is done by the gas during this expansion?

A) $10.4 \mathrm { MJ }$
B) $3.85 \mathrm { MJ }$
C) $3.85 \mathrm {~kJ}$
D) $10.4 \mathrm {~kJ}$
E) $3850 \mathrm {~kJ}$

Question 37

Write the word or phrase that best completes each statement or answers the question.
A heat engine receives $7000 \mathrm {~J}$ of heat and loses $3000 \mathrm {~J}$ in each cycle. What is the efficiency of this engine?

A) $70 \%$
B) $30 \%$
C) $57 \%$
D) $43 \%$

Question 38

Write the word or phrase that best completes each statement or answers the question.
A certain heat engine extracts $1.30 \mathrm {~kJ}$ of heat from a hot temperature reservoir and discharges $0.70$ $\mathrm { kJ }$ of heat to a cold temperature reservoir. What is the efficiency of this engine?

A) $13 \%$
B) $27 \%$
C) $54 \%$
D) $86 \%$
E) $46 \%$

Question 39

Choose the one alternative that best completes the statement or answers the question.
A monatomic ideal gas undergoes an isothermal expansion at $300 \mathrm {~K}$ , as the volume increased from $0.010 \mathrm {~m} ^ { 3 }$ to $0.040 \mathrm {~m} ^ { 3 }$ . The final pressure is $130 \mathrm { kPa }$ . What is the change in the internal (thermal) energy of the gas during this process? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

A) $3.6 \mathrm {~kJ}$
B) $- 7.2 \mathrm {~kJ}$
C) $- 3.6 \mathrm {~kJ}$
D) $7.2 \mathrm {~kJ}$
E) $0.0 \mathrm {~kJ}$

Question 40

Choose the one alternative that best completes the statement or answers the question.
An expansion process on an ideal diatomic ideal gas has a linear path between the initial and final coordinates on a $p V$ diagram. The coordinates of the initial state are: the pressure is $300 \mathrm { kPa }$ , the volume is $0.0700 \mathrm {~m} ^ { 3 }$ , and the temperature is $390 \mathrm {~K}$ . The final pressure is $130 \mathrm { kPa }$ and the final temperature is $310 \mathrm {~K}$ . How much work is done by the gas during this process? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

A) $19,000 \mathrm {~J}$
B) $13,000 \mathrm {~J}$
C) $6300 \mathrm {~J}$
D) $16,000 \mathrm {~J}$
E) $9400 \mathrm {~J}$

Question 41

Choose the one alternative that best completes the statement or answers the question.
An ideal Carnot engine operates between a warm reservoir at $233 \mathrm {~K}$ and a colder reservoir. During each cycle, this engine extracts $15.0 \mathrm {~J}$ of heat from the warm reservoir and does $4.0 \mathrm {~J}$ of work. What is the temperature of the colder reservoir?

A) $47 \mathrm {~K}$
B) $67 \mathrm {~K}$
C) $62 \mathrm {~K}$
D) $171 \mathrm {~K}$

Question 42

Write the word or phrase that best completes each statement or answers the question.
An inventor tries to sell you his new heat engine that takes in $40 \mathrm {~J}$ of heat at $87 ^ { \circ } \mathrm { C }$ on each cycle, expels $30 \mathrm {~J}$ at $27 ^ { \circ } \mathrm { C }$ , and does $10 \mathrm {~J}$ of work. Would it be wise to invest in this engine? Back up your conclusion with numerical calculations.

Question 43

Choose the one alternative that best completes the statement or answers the question.
What is the efficiency of an ideal Carnot engine operating between a reservoir in which ice and water coexist, and a reservoir in which water and steam coexist? The pressure is constant at $1.0$ atm for both reservoirs.

A) $100 \%$
B) $1.0 \%$
C) $0.27 \%$
D) $15 \%$
E) $27 \%$

Question 44

Write the word or phrase that best completes each statement or answers the question.
A heat engine absorbs 85.6 kJ of heat each cycle and exhausts 61.8 kJ.
(a) What is the efficiency of the engine?
(b) How much work does it do each cycle?

Question 45

Write the word or phrase that best completes each statement or answers the question.
An ideal Carnot engine is operated between a hot and a cold reservoir. The temperature difference between the two reservoirs is $284 ^ { \circ } \mathrm { C }$ . If the efficiency of this ideal engine is $24.0 \%$ , find the temperature of the cold reservoir in degrees Celsius.

Question 46

Write the word or phrase that best completes each statement or answers the question.
A gas follows the $p V$ trajectory shown in Figure 16.2. How much work is done per cycle by the gas if The gas in a heat engine follows the cycle shown in the $p V$ diagram. How much work does this engine do each cycle if $p _ { 0 } = 5.4$ atm?

A) $1100 \mathrm {~J}$
B) $870 \mathrm {~J}$
C) $440 \mathrm {~J}$
D) $220 \mathrm {~J}$

Question 47

Choose the one alternative that best completes the statement or answers the question.
For a certain ideal Carnot engine, the hot reservoir is $35 \mathrm { C } ^ { \circ }$ higher than the cold reservoir. If this engine is to have an efficiency of $20 \%$ , what must be the temperature of the hot reservoir?

A) $245 \mathrm {~K}$
B) $210 \mathrm {~K}$
C) $70.0 \mathrm {~K}$
D) $140 \mathrm {~K}$
E) $175 \mathrm {~K}$

Question 48

Write the word or phrase that best completes each statement or answers the question.
An ideal Carnot heat engine operates between reservoirs at 1740 K and 150 K. In each
cycle, 260 J of heat energy is rejected to the low temperature reservoir. In each cycle, how
much mechanical work W is performed by the engine?

Question 49

Write the word or phrase that best completes each statement or answers the question.
A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of 450 $\mathrm { K }$ and $270 \mathrm {~K}$ , performs $3.3 \mathrm {~kJ}$ of net work, and rejects $8.2 \mathrm {~kJ}$ of heat in a single cycle.
(a) What is the thermal efficiency of this heat engine?
(b) What is the maximum efficiency it could possibly have?

Question 50

Choose the one alternative that best completes the statement or answers the question.
An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at $1.76 \mathrm {~K}$ has an efficiency of $40.0 \%$ . What is the temperature of the warm reservoir?

A) $106 \mathrm {~K}$
B) $0.0400 \mathrm {~K}$
C) $0.0500 \mathrm {~K}$
D) $2.93 \mathrm {~K}$

Question 51

Choose the one alternative that best completes the statement or answers the question.
The ocean thermal energy conversion project uses the surface water near tropical islands with a temperature of $20 ^ { \circ } \mathrm { C }$ as the hot temperature reservoir, and the water at some depth, with a temperature of $5.0 ^ { \circ } \mathrm { C }$ , as the cold temperature reservoir for a heat engine. What is the maximum possible efficiency of an engine running between those two temperatures?

A) $7.9 \%$
B) $4.7 \%$
C) $30 \%$
D) $5.1 \%$
E) $15 \%$

Question 52

Choose the one alternative that best completes the statement or answers the question.
Two ideal Carnot heat engines have the same efficiency. One operates between $5.0 \times 10 ^ { 2 } \mathrm {~K}$ and $3.0$ $\times 10 ^ { 2 } \mathrm {~K}$ , and the other between $4.0 \times 10 ^ { 2 } \mathrm {~K}$ and some lower temperature. What is the lower temperature?

A) $280 \mathrm {~K}$
B) $240 \mathrm {~K}$
C) $200 \mathrm {~K}$
D) $220 \mathrm {~K}$
E) $260 \mathrm {~K}$

Question 53

Write the word or phrase that best completes each statement or answers the question.
A coal-fired plant generates $600 \mathrm { MW }$ of electric power. The plant uses $4.8 \times 10 ^ { 6 } \mathrm {~kg}$ of coal each day, and the heat of combustion of coal is $3.3 \times 10 ^ { 7 } \mathrm {~J} / \mathrm { kg }$ . The steam that drives the turbines is at a temperature of $300 ^ { \circ } \mathrm { C }$ , and the exhaust water is at $37 ^ { \circ } \mathrm { C }$ .
(a) What is the overall efficiency of the plant for generating electric power?
(b) How much thermal energy is exhausted each day?
(c) Using the same heat reservoirs, what is the maximum possible efficiency for a heat engine?

Question 54

Choose the one alternative that best completes the statement or answers the question.
An ideal Carnot engine operates between a high temperature reservoir at $492 \mathrm {~K}$ and a river with water at $290 \mathrm {~K}$ . If it absorbs $4000 \mathrm {~J}$ of heat each cycle, how much work per cycle does it perform?

A) $2358 \mathrm {~J}$
B) $1483 \mathrm {~J}$
C) $1642 \mathrm {~J}$
D) $2517 \mathrm {~J}$

Question 55

Choose the one alternative that best completes the statement or answers the question.
A Carnot engine operates between two reservoirs with unknown temperatures. If the Carnot engine operates at $67 \%$ efficiency, what is the ratio of the absolute temperatures of the reservoirs, $T _ { d } T _ { h }$ ?

A) $0.0012$
B) $0.0025$
C) $0.67$
D) $0.33$

Question 56

Choose the one alternative that best completes the statement or answers the question.
An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at $1.76 \mathrm {~K}$ has an efficiency of $11.0 \%$ . What is the temperature of the warm reservoir?

A) $1.98 \mathrm {~K}$
B) $157 \mathrm {~K}$
C) $0.160 \mathrm {~K}$
D) $0.180 \mathrm {~K}$

Question 57

Write the word or phrase that best completes each statement or answers the question.
One of the most efficient engines built so far has the following characteristics: The combustion chamber temperature is $1900 ^ { \circ } \mathrm { C }$ , the exhaust temperature $= 430 ^ { \circ } \mathrm { C } , 7.0 \times 10 ^ { 9 }$ cal of fuel produces $1.4 \times 1010 \mathrm {~J}$ of work in one hour. ( $1 \mathrm { cal } = 4.186 \mathrm {~J}$ )
(a) What is the actual efficiency of this engine?
(b) What is the power output of this engine?
(c) What would be the maximum possible efficiency for an engine using the same temperature extremes?

Question 58

Write the word or phrase that best completes each statement or answers the question.
The figure shows a $p V$ diagram for a cycle of a heat engine for which $Q \mathrm { H } = 59 \mathrm {~J}$ . What is the thermal efficiency of the engine?

A) $17 \%$
B) $34 \%$
C) $14 \%$
D) $8.5 \%$

Question 59

Choose the one alternative that best completes the statement or answers the question.
An ideal Carnot heat engine operates between $285 \mathrm {~K}$ and $460 \mathrm {~K}$ . What is its efficiency?

A) $0.62$
B) $1.61$
C) $0.38$
D) $0.61$

Question 60

Write the word or phrase that best completes each statement or answers the question.
A heat engine has an efficiency of 31.4% and receives 8.72 kJ of heat per cycle.
(a) How much work does it perform in each cycle?
(b) How much heat does it exhaust in each cycle?

Question 61

Choose the one alternative that best completes the statement or answers the question.
On a cold winter day, the outside temperature is $- 20 ^ { \circ } \mathrm { C }$ and the inside temperature is maintained at $20 ^ { \circ } \mathrm { C }$ . There is a net heat flow to the outside through the walls, roof, etc., of $25 \mathrm {~kW}$ . At what rate is the entropy of the air outside the house changing as a result of this process?

A) $+ 13 \mathrm {~W} / \mathrm { K }$
B) $0 \mathrm {~W} / \mathrm { K }$
C) $- 25 \mathrm {~W} / \mathrm { K }$
D) $+ 99 \mathrm {~W} / \mathrm { K }$
E) $85 \mathrm {~W} / \mathrm { K }$

Question 62

Write the word or phrase that best completes each statement or answers the question.
A reversible engine takes in heat at a rate of 555 W and exhausts heat at 482 W.
(a) How much power does it produce?
(b) What is its efficiency?
(c) If operated in reverse as a refrigerator, what would be its performance coefficient
(COP)?

Question 63

Choose the one alternative that best completes the statement or answers the question.
What is the change in entropy when $15.0 \mathrm {~g}$ of water at $100 ^ { \circ } \mathrm { C }$ are turned into steam at $100 ^ { \circ } \mathrm { C }$ ? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ .

A) $0 \mathrm {~J} / \mathrm { K }$
B) $- 90.8 \mathrm {~J} / \mathrm { K }$
C) $339 \mathrm {~J} / \mathrm { K }$
D) $90.8 \mathrm {~J} / \mathrm { K }$
E) $- 339 \mathrm {~J} / \mathrm { K }$

Question 64

Write the word or phrase that best completes each statement or answers the question.
A refrigerator has a performance coefficient (COP) of $1.15$ , and it extracts $7.95 \mathrm {~J}$ of heat from the cold reservoir during each cycle.
(a) How much work is done on the gas in each cycle?
(b) How much heat is exhausted into the hot reservoir in each cycle?

Question 65

Choose the one alternative that best completes the statement or answers the question.
An irreversible engine operating between the temperatures of $550 \mathrm {~K}$ and $300 \mathrm {~K}$ extracts $1.20 \mathrm {~kJ}$ of heat from the hot reservoir and produces $0.450 \mathrm {~kJ}$ of work. How much entropy is created in the process?

A) $0.68 \mathrm {~J} / \mathrm { K }$
B) $0.44 \mathrm {~J} / \mathrm { K }$
C) $0.32 \mathrm {~J} / \mathrm { K }$
D) $0 \mathrm {~J} / \mathrm { K }$
E) $0.73 \mathrm {~J} / \mathrm { K }$

Question 66

Choose the one alternative that best completes the statement or answers the question.
When $0.50 \mathrm {~kg}$ of water at $0 ^ { \circ } \mathrm { C }$ freezes, what is the change in entropy of the water? The latent heat of fusion of water is $33,400 \mathrm {~J} / \mathrm { kg }$ .

A) $610 \mathrm {~J} / \mathrm { K }$
B) $- 610 \mathrm {~J} / \mathrm { K }$
C) $0 \mathrm {~J} / \mathrm { K }$
D) $- 17,000 \mathrm {~J} / \mathrm { K }$
E) $17,000 \mathrm {~J} / \mathrm { K }$

Question 67

Write the word or phrase that best completes each statement or answers the question.
If the efficiency of a reversible engine is 28%, what is its COP (performance coefficient)
operated (a) as a refrigerator, and (b) as a heat pump?

Question 68

Choose the one alternative that best completes the statement or answers the question.
A container of ideal gas at STP undergoes an isothermal expansion and its entropy changes by $3.7$ $\mathrm { J } / \mathrm { K }$ . How much work does it do?

A) $1.4 \times 10 ^ { 3 } \mathrm {~J}$
B) $0.0 \mathrm {~J}$
C) $1.0 \times 10 ^ { 3 } \mathrm {~J}$
D) $- 1.4 \times 10 ^ { 3 } \mathrm {~J}$
E) $- 1.0 \times 10 ^ { 3 } \mathrm {~J}$

Question 69

Choose the one alternative that best completes the statement or answers the question.
On a cold winter day, the outside temperature is $- 20 ^ { \circ } \mathrm { C }$ and the inside temperature is maintained at $20 ^ { \circ } \mathrm { C }$ . There is a net heat flow to the outside through the walls, roof, etc., of $25 \mathrm {~kW}$ . What is the rate of increase of the entropy of the universe as a result of this heat flow?

A) $99 \mathrm {~W} / \mathrm { K }$
B) $13 \mathrm {~W} / \mathrm { K }$
C) $25 \mathrm {~W} / \mathrm { K }$
D) $0 \mathrm {~W} / \mathrm { K }$
E) $85 \mathrm {~W} / \mathrm { K }$

Question 70

Write the word or phrase that best completes each statement or answers the question.
What is the entropy change of $450 \mathrm {~g}$ of water when it changes from (a) liquid to steam at its usual boiling point and (b) ice to liquid at its usual melting point? For water, $L _ { F } = 0.334$ $\mathrm { MJ } / \mathrm { kg } , L \mathrm {~V} = 2.26 \mathrm { MJ } / \mathrm { kg }$ .

Question 71

Choose the one alternative that best completes the statement or answers the question.
When $1.0 \mathrm {~kg}$ of steam at $100 ^ { \circ } \mathrm { C }$ condenses to water at $100 ^ { \circ } \mathrm { C }$ , what is the change in entropy of the steam? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ .

A) $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { K }$
B) $- 6.1 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { K }$
C) zero
D) $6.1 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { K }$
E) $- 22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { K }$

Question 72

Choose the one alternative that best completes the statement or answers the question.
A 0.42-kg quantity of ethanol, in the liquid state at its melting point of $- 114.4 ^ { \circ } \mathrm { C }$ , is frozen at atmospheric pressure. The heat of fusion of ethanol is $1.04 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ , and its molecular mass is $46.1 \mathrm {~g} / \mathrm { mol }$ . What is the change in the entropy of the ethanol as it freezes?

A) $280 \mathrm {~J} / \mathrm { K }$
B) $250 \mathrm {~J} / \mathrm { K }$
C) $- 280 \mathrm {~J} / \mathrm { K }$
D) $- 250 \mathrm {~J} / \mathrm { K }$
E) $- 310 \mathrm {~J} / \mathrm { K }$

Question 73

Write the word or phrase that best completes each statement or answers the question.
What is the change in entropy of the ice when a $0.050 - \mathrm { kg }$ ice cube at $0 ^ { \circ } \mathrm { C }$ melts? The latent heat of fusion for water is $80 \mathrm { cal } / \mathrm { g }$ .

Question 74

Write the word or phrase that best completes each statement or answers the question.
A 15.0-kg block of ice at 0.00°C falls into Lake Superior, which is a fresh water lake. The
lake water is at 10.0°C, and the latent heat of fusion for ice is 3.34 × 105 J/kg. Find the
change in entropy due to the melting of the ice (a) of the block of ice, (b) of the lake, and (c)
of the system consisting of the lake and the ice. (d) Is your answer to part (c) consistent
with the reversibility or irreversibility of the melting process?

Question 75

Write the word or phrase that best completes each statement or answers the question.
An ideal Carnot refrigerator powered from an electrical outlet takes heat from water at $0.0 ^ { \circ } \mathrm { C }$ and rejects heat to a room at $20.0 ^ { \circ } \mathrm { C }$ . How much electrical energy must be supplied to the refrigerator so it will convert $78 \mathrm {~g}$ of water at $0.0 ^ { \circ } \mathrm { C }$ to ice at $0.0 ^ { \circ } \mathrm { C }$ . The latent heat of fusion of water is $3.34 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ .

Question 76

Write the word or phrase that best completes each statement or answers the question.
An ideal Carnot refrigerator with a performance coefficient (COP) of $5.0$ cools items inside of it to $5.0 ^ { \circ } \mathrm { C }$ . What is the high temperature needed to operate this refrigerator?

A) $1395 ^ { \circ } \mathrm { C }$
B) $30 ^ { \circ } \mathrm { C }$
C) $61 ^ { \circ } \mathrm { C }$
D) $6 ^ { \circ } \mathrm { C }$

Question 77

Write the word or phrase that best completes each statement or answers the question.
What is the change in entropy of the lead when $2.0 \mathrm {~kg}$ of molten lead at its melting point temperature solidifies? For lead: $L _ { V } = 207 \mathrm { kcal } / \mathrm { kg }$ at $1744 ^ { \circ } \mathrm { C } , L F = 5.9 \mathrm { kcal } / \mathrm { kg }$ at $328 ^ { \circ } \mathrm { C }$ .

Question 78

Write the word or phrase that best completes each statement or answers the question.
During each cycle, a refrigerator removes $20.0 \mathrm {~kJ}$ of heat from the freezing compartment and ejects $24.0 \mathrm {~kJ}$ into a room.
(a) How much work per cycle is required each cycle to run this refrigerator?
(b) What is the coefficient of performance of this refrigerator?