# Quiz 17: Work, Heat, and the First Law of Thermodynamics

Physics & Astronomy

98

All Questions

85

Multiple Choice

0

True False

5

Essay

8

Short Answer

0

Not Answered

Q 1

When a gas undergoes an isothermal process, there is
A) no change in the pressure of the gas.
B) no change in the temperature of the gas.
C) no change in the volume of the gas.
D) no work done by (or on) the gas.
E) no heat added to the gas.

Free

Multiple Choice

B

Q 2

An ideal gas is compressed in a well-insulated chamber using a well-insulated piston. This process is
A) isochoric.
B) isothermal.
C) adiabatic.
D) isobaric.

Free

Multiple Choice

C

Q 3

The process shown in the T-V diagram in the figure is an
A) adiabatic compression.
B) isothermal compression.
C) isochoric compression.
D) isobaric compression.
E) isothermal expansion.

Free

Multiple Choice

B

Q 4

The process shown in the pV diagram in the figure is an
A) adiabatic expansion.
B) isothermal expansion.
C) isochoric expansion.
D) isobaric expansion.
E) isochoric compression.

Multiple Choice

Q 5

The process shown in the pV diagram in the figure is
A) adiabatic.
B) isothermal.
C) isochoric.
D) isobaric.

Multiple Choice

Q 6

When a fixed amount of ideal gas goes through an isothermal expansion
A) its internal (thermal) energy does not change.
B) the gas does no work.
C) no heat enters or leaves the gas.
D) its temperature must decrease.
E) its pressure must increase.

Multiple Choice

Q 7

When a fixed amount of ideal gas goes through an adiabatic expansion
A) its internal (thermal) energy does not change.
B) the gas does no work.
C) no heat enters or leaves the gas.
D) its temperature cannot change.
E) its pressure must increase.

Multiple Choice

Q 8

When a fixed amount of ideal gas goes through an isobaric expansion
A) its internal (thermal) energy does not change.
B) the gas does no work.
C) no heat enters or leaves the gas.
D) its temperature must increase.
E) its pressure must increase.

Multiple Choice

Q 9

When a fixed amount of ideal gas goes through an isochoric process
A) its internal (thermal) energy does not change.
B) the gas does no work.
C) no heat enters or leaves the gas.
D) its temperature must increase.
E) its pressure must increase.

Multiple Choice

Q 10

An ideal gas increases in temperature from 22°C to 42°C by two different processes. In one process, the temperature increases at constant volume, and in the other process the temperature increases at constant pressure. Which of the following statements about this gas are correct? (There may be more than one correct choice.)
A) The heat required to cause this temperature change is the same for both the constant-volume and the constant-pressure processes.
B) More heat is required for the constant-pressure process than for the constant-volume process.
C) The change in the internal (thermal) energy of the gas is the same for both the constant-volume and the constant-pressure processes.
D) The root-mean-square (thermal) speed of the gas molecules increases more during the constant-volume process than during the constant-pressure process.

Multiple Choice

Q 11

A container of ideal gas has a movable frictionless piston. This container is placed in a very large water bath and slowly compressed so that the temperature of the gas remains constant and equal to the temperature of the water. Which of the following statements about this gas are true for this process? (There may be more than one correct choice.)
A) Heat leaves the gas during the compression.
B) Since the gas and water are at the same temperature, no heat can flow between them, which makes this an adiabatic compression.
C) The internal (thermal) energy of the gas does not change during the compression.
D) The internal energy of the gas increases during the compression because work is done on the gas.
E) Since the temperature of the gas remains constant, the pressure of the gas must also remain constant.

Multiple Choice

Q 12

When an ideal gas increases in volume at constant pressure, the average kinetic energy of the gas molecules
A) increases.
B) decreases.
C) does not change.
D) may either increase or decrease, depending on whether or not the process is carried out adiabatically.
E) may or may not change, but insufficient information is given to make such a determination.

Multiple Choice

Q 13

It is a well-known fact that water has a higher specific heat than iron. Now, consider equal masses of water and iron that are initially in thermal equilibrium. The same amount of heat, 30 calories, is added to each one. Which statement is true?
A) They remain in thermal equilibrium.
B) They are no longer in thermal equilibrium; the iron is warmer.
C) They are no longer in thermal equilibrium; the water is warmer.
D) It is impossible to say without knowing the exact mass involved.
E) It is impossible to say without knowing the exact specific heats.

Multiple Choice

Q 14

A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper; the aluminum and the copper are in thermal contact. The specific heat of aluminum is more than double that of copper. Which object experiences the greater temperature change during the time the system takes to reach thermal equilibrium?
A) The copper experiences a greater temperature change.
B) The aluminum experiences a greater temperature change.
C) Neither; both objects experience the same magnitude temperature change.
D) It is impossible to tell without knowing the masses.
E) It is impossible to tell without knowing the volumes.

Multiple Choice

Q 15

When a solid melts
A) the temperature of the substance increases.
B) the temperature of the substance decreases.
C) heat energy leaves the substance.
D) heat energy enters the substance.

Multiple Choice

Q 16

When a vapor condenses
A) the temperature of the substance increases.
B) the temperature of the substance decreases.
C) heat energy leaves the substance.
D) heat energy enters the substance.

Multiple Choice

Q 17

A chunk of ice (T = -20°C) is added to a thermally insulated container of cold water (T = 0°C). What happens in the container?
A) The ice melts until thermal equilibrium is established.
B) The water cools down until thermal equilibrium is established.
C) Some of the water freezes and the chunk of ice gets larger.
D) None of the above things happen.

Multiple Choice

Q 18

The figure (not to scale) shows a pV diagram for 1.8 g of helium gas (He) that undergoes the process 1 → 2 → 3. Find the value of V

_{3}. The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the atomic weight of helium is 4.0 g/mol. A) 17 L B) 69 L C) 34 L D) 8.6 L Multiple Choice

Q 19

The figure shows a pV diagram for 8.3 g of nitrogen gas (N

_{2}) in a sealed container. The temperature T_{1}of the gas in state 1 is 79°C. What are (a) the pressure p_{1}of the gas in state 1 and (b) the temperature T_{2}of the gas in state 2? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the ATOMIC weight of nitrogen is 14 g/mol. A) (a) 86 atm, (b) 700°C. B) (a) 19 atm, (b) 700°C. C) (a) 86 atm, (b) 160°C. D) (a) 19 atm, (b) 160°C. Multiple Choice

Q 20

The figure shows a pV diagram for 4.3 g of oxygen gas (O

_{2}) in a sealed container. The temperature T_{1}of the gas in state 1 is 21°C. What are the temperatures T_{3}and T_{4}of the gas in states 3 and 4? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the ATOMIC weight of oxygen is 16 g/mol. A) -52°C, 390°C B) 16°C, 47°C C) 220°C, 660°C D) 11°C, 32°C Multiple Choice

Q 21

The figure shows a pV diagram for 0.95 mol of gas that undergoes the process 1 → 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? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.
A) -160°C
B) 15°C
C) 390°C
D) 120°C

Multiple Choice

Q 22

The figure shows a pV diagram for 0.0066 mol of gas that undergoes the process 1 → 2 → 3. What is the pressure p

_{2}. The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K. A) 5.3 atm B) 5.3 × 10^{5}_{ atm}C) 16 atm D) 1.6 × 10^{6}_{ atm} Multiple Choice

Q 23

How much work is done by 3.00 mol of ideal gas when it triples its volume at a constant temperature of 127°C? The ideal gas constant is R = 8.314 J/mol ∙ K.
A) 12.7 kJ
B) 9.97 kJ
C) 11.0 kJ
D) 15.3 kJ
E) 1.20 kJ

Multiple Choice

Q 24

An ideal gas in a balloon is kept in thermal equilibrium with its constant-temperature surroundings. How much work is done by the gas if the outside pressure is slowly reduced, allowing the balloon to expand to 6.0 times its original size? The balloon initially has a pressure of 645.0 Pa and a volume of 0.10 m

^{3}. The ideal gas constant is R = 8.314 J/mol ∙ K. A) 120 J B) 390 J C) -330 J D) 6.0 J Multiple Choice

Q 25

A steel container, equipped with a piston, contains 21 mol of an ideal gas at 465 K. The container is compressed isothermally to 90% of its original volume. How much work is done on the gas? The ideal gas constant is R = 8.314 J/mol ∙ K.
A) 8600 J
B) -73,300 J
C) -8500 J
D) 11 J

Multiple Choice

Q 26

A certain amount of ideal monatomic gas is maintained at constant volume as it is cooled from 455K to 405 K. This feat is accomplished by removing 400 J of heat from the gas. How much work is done by the gas during this process? The ideal gas constant is R = 8.314 J/mol ∙ K.
A) 0.00 J
B) 200 J
C) 400 J
D) -400 J
E) -200 J

Multiple Choice

Q 27

An ideal monatomic gas cools from 455.0 K to 405.0 K at constant volume as 831 J of energy is removed from it. How many moles of gas are in the sample? The ideal gas constant is R = 8.314 J/mol ∙ K.
A) 2.50 mol
B) 2.15 mol
C) 1.50 mol
D) 1.33 mol
E) 0.725 mol

Multiple Choice

Q 28

3.0 moles of an ideal gas with a molar heat capacity at constant volume of 4.9 cal/(mol∙K) and a molar heat capacity at constant pressure of 6.9 cal/(mol∙K) starts at 300 K and is heated at constant pressure to 320 K, then cooled at constant volume to its original temperature. How much heat flows into the gas during this two-step process?
A) 710 cal
B) -720 cal
C) 0.00 cal
D) 120 cal
E) -120 cal

Multiple Choice

Q 29

A quantity of ideal gas requires 800 kJ to raise the temperature of the gas by 10.0 K when the gas is maintained at constant volume. The same quantity of gas requires 900 kJ to raise the temperature of the gas by 10.0 K when the gas is maintained at constant pressure. What is the adiabatic constant γ for this gas?
A) 0.889
B) 1.13
C) 1.22
D) 1.67
E) 1.40

Multiple Choice

Q 30

The temperature of an ideal gas in a sealed 0.40-m

^{3}rigid container is reduced from 350 K to 270 K. The final pressure of the gas is 60 kPA. The molar heat capacity at constant volume of the gas is 28.0 J/mol · K. The heat absorbed by the gas is closest to A) -24 kJ. B) -31 kJ. C) 24 kJ. D) 31 kJ. E) 0.00 kJ. Multiple Choice

Q 31

The temperature of an ideal gas in a sealed 0.40 m

^{3}container is reduced from 400 K to 270 K. The final pressure of the gas is 30 kPA. The molar heat capacity at constant volume of the gas is 28.0 J/mol · K. The work done by the gas is closest to A) 0.00 kJ. B) -19 kJ. C) -25 kJ. D) 19 kJ. E) 25 kJ. Multiple Choice

Q 32

A compression, at a constant pressure of 190 kPa, is performed on 5.0 moles of an ideal monatomic gas. The compression reduces the volume of the gas from 0.19 m

^{3}to 0.12 m^{3}. The ideal gas constant is R = 8.314 J/mol ∙ K.^{ }The work done by the gas is closest to A) -13 kJ. B) 13 kJ. C) -33 kJ. D) 33 kJ. E) 0.00 kJ. Multiple Choice

Q 33

A monatomic ideal gas undergoes an isothermal expansion at 300 K, as the volume increased from 0.03 m

^{3}to 0.21 m^{3}. The final pressure of the gas is 60 kPA The ideal gas constant is R = 8.314 J/mol ∙ K. The change in the internal (thermal) energy of the gas is closest to A) 0.00 kJ. B) 12 kJ. C) 25 kJ. D) -12 kJ. E) -25 kJ. Multiple Choice

Q 34

A monatomic ideal gas undergoes an isothermal expansion at 300 K, as the volume increased from 0.020 m

^{3}to 0.040 m^{3}. The final pressure is 120 kPa. The ideal gas constant is R = 8.314 J/mol ∙ K. The heat transfer to the gas is closest to A) 3.3 kJ. B) 1.7 kJ. C) -3.3 kJ. D) -1.7 kJ. E) 0.00 kJ. Multiple Choice

Q 35

An expansion process on an ideal diatomic gas has a linear path between the initial and final states on a pV diagram. The initial pressure is 300 kPa, the initial volume is 0.060 m

^{3}, and the initial temperature is 390 K. The ideal gas constant is R = 8.314 J/mol ∙ K. The final pressure is 150 kPa and the final temperature is 260 K. The work done by the gas is closest to A) 4500 J. B) 2300 J. C) 3400 J. D) 5600 J. E) 6800 J. Multiple Choice

Q 36

An expansion process on an ideal diatomic gas has a linear path between the initial and final states on a pV diagram. The initial pressure is 300 kPa, the initial volume is 0.020 m

^{3}, and the initial temperature is 390 K. The final pressure is 160kPa and the final temperature is 310 K. The change in the internal (thermal) energy of the gas is closest to A) -3100 J. B) -1800 J. C) 3100 J. D) 1800 J. E) 0.00 J. Multiple Choice

Q 37

An adiabatic compression is performed on an ideal gas. The final pressure is equal to 0.560 times the initial pressure and the final volume equals 1.50 times the initial volume. What is the adiabatic constant for the gas?
A) 1.33
B) 1.43
C) 1.48
D) 1.52
E) 1.67

Multiple Choice

Q 38

An ideal gas with γ = 1.67 is initially at 0°C in a volume of 10.0 L at a pressure of 1.00 atm. It is then expanded adiabatically to a volume of 10.4 L. What is the final temperature of the gas?
A) -7.1°C
B) 2.5°C
C) -23°C
D) 68°C
E) -20°C

Multiple Choice

Q 39

During an isothermal process, 5.0 J of heat is removed from an ideal gas. What is the change in internal (thermal) energy of the gas?
A) 0.00 J
B) 2.5 J
C) 5.0 J
D) 7.5 J
E) 10 J

Multiple Choice

Q 40

During an isothermal process, 5.0 J of heat is removed from an ideal gas. How much work does the gas do during this process?
A) 0.00 J
B) 2.0 J
C) 5.0 J
D) -5.0 J
E) 10 J

Multiple Choice

Q 41

During an adiabatic process, an ideal gas does 25 J of work. What is the change in the internal (thermal) energy of the gas during this process?
A) 0.00 J
B) 50 J
C) 25 J
D) -25 J
E) -50 J

Multiple Choice

Q 42

In an isochoric process, the internal (thermal) energy of an ideal gas decreases by 50 J. How much work does the gas do during this process?
A) 0.00 J
B) 25 J
C) 50 J
D) -25 J
E) -50 J

Multiple Choice

Q 43

In an isochoric process, the internal (thermal) energy of an ideal gas decreases by 50 J. How much heat is exchanged with the gas during this process?
A) 0.00 J
B) 25 J
C) 50 J
D) -25 J
E) -50 J

Multiple Choice

Q 44

A system has a heat source supplying heat to an ideal gas at a rate of 187.0 W and the gas is doing work at a rate of 130.9 W. At what rate is the internal (thermal) energy of the gas changing?
A) 56.1 W
B) 318 W
C) -56.1 W
D) 187 W

Multiple Choice

Q 45

The gas in a perfectly insulated system does work at a rate of 13 W. At what rate is the internal (thermal) energy of the gas changing?
A) -13 W
B) 13 W
C) 0.00 W
D) 6.5 W

Multiple Choice

Q 46

An ideal gas is allowed to expand slowly at constant temperature to twice its original volume. During the expansion, the gas absorbs 200 kJ of heat.
(a) What is the change in the internal (thermal) energy of the gas during the expansion?
(b) How much work does the gas do during the expansion?

Essay

Q 47

An ideal gas initially at 300 K and occupying a volume of 20 L is adiabatically compressed. If its final temperature is 400 K and γ = 1.30, what is its final volume?
A) 7.7 L
B) 14 L
C) 22 L
D) 52 L

Multiple Choice

Q 48

A container with rigid walls is filled with 4 mol of air with C

_{V}= 2.5R. How much does the internal (thermal) energy change if the temperature of the air rises from 16°C to 437°C? The ideal gas constant is R = 8.314 J/mol ∙ K. A) 35 kJ B) 421 J C) 3.5 kJ D) 8.75 kJ Multiple Choice

Q 49

An ideal gas with γ = 1.30 occupies 7.0 L at 300 K and 200 kPa pressure. It is compressed adiabatically to 1/7 of its original volume, then cooled at constant volume to 300 K, and finally allowed to expand isothermally to 7.0 L. How much work does the gas do during this process? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.
A) -980 J
B) 6400 J
C) -270,000 J
D) -6400 J
E) 980 J

Multiple Choice

Q 50

The pV diagram shown is for 7.50 moles of an ideal diatomic gas taken through a cycle from a to b to c. The ideal gas constant is R = 8.314 J/mol ∙ K.
(a) What is the highest temperature reached by the gas during the cycle?
(b) What net work does the gas do during the cycle?
(c) How much heat is exchanged with the gas during part bc of the cycle? Does it enter or leave the gas?
(d) What is the change in the internal (thermal) energy of the gas during part bc of the cycle?
(e) What is the change in the internal (thermal) energy of the gas during the entire cycle?

Essay

Q 51

A cylinder contains 23 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.43 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol · K and the ideal gas constant is R = 8.314 J/mol ∙ K. The heat absorbed by the gas is closest to
A) -130 kJ.
B) -94 kJ.
C) 130 kJ.
D) 94 kJ.
E) -33 kJ.

Multiple Choice

Q 52

A cylinder contains 24.0 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.63 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol · K and the ideal gas constant is R = 8.314 J/mol ∙ K. The change in the internal (thermal) energy of the gas is closest to
A) -64 kJ.
B) -86 kJ.
C) 64 kJ.
D) 86 kJ.
E) -22 kJ.

Multiple Choice

Q 53

During an adiabatic process, 20 moles of a monatomic ideal gas undergo a temperature change from 450 K to 320 K starting from an initial pressure is 400 kPa. The ideal gas constant is R = 8.314 J/mol ∙ K.
(a) What is the final volume of the gas?
(b) How much heat does the gas exchange during this process?
(c) What is the change in the internal (thermal) energy of the gas during this process?

Essay

Q 54

The figure shows the pV diagram for a certain thermodynamic process. In this process, 1500 J of heat flows into a system, and at the same time the system expands against a constant external pressure of 9.00 x 10

^{4}Pa. If the volume of the system increases from 0.020 m^{3}to 0.050 m^{3}, calculate the change in internal (thermal) energy of the system. If the internal (thermal) energy change is nonzero, be sure to indicate whether this energy change is positive or negative. Short Answer

Q 55

A fixed amount of ideal gas goes through a process abc. In state a, the temperature of the gas is 152°C, its pressure is 1.25 atm, and it occupies a volume of 0.250 m

^{3}. It then undergoes an isothermal expansion to state b that doubles its volume, followed by an isobaric compression back to its original volume at state c. (Hint: First show this process on a pV diagram.) The ideal gas constant is 8.314 J/mol ∙ K, and 1.00 atm = 1.01 × 10^{5}Pa. (a) How many moles does this gas contain? (b) What is the change in the internal energy of the gas between states a and b? (c) What is the net work done on (or by) this gas during the entire process? (d) What is the temperature of the gas in state c? Essay

Q 56

A cylinder contains 1.2 moles of ideal gas, initially at a temperature of 116°C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of 6.4 x 10

^{5}Pa on the gas. The gas is cooled until its temperature has decreased to 27°C For the gas and the ideal gas constant (a) Find the work done by (or on) the gas during this process. Is the work done by or on the gas? (b) What is the change in the internal (thermal) energy of the gas during this process? (c) How much heat is transferred to (or from) the gas during this process? Does this heat flow into or out of the gas? Essay

Q 57

In a thermodynamic process involving 7.8 moles of an ideal gas, the gas is at an initial temperature of 24°C and has an initial volume of 0.040 m

^{3}. The gas expands adiabatically to a volume of 0.080 m^{3}. For this gas, C_{V}= 12.27 J/mol · K, and the ideal gas constant is R = 8.314 J/mol ∙ K. Calculate the work done by the gas during this expansion. Short Answer

Q 58

It is necessary to determine the specific heat of an unknown object. The mass of the object is measured to be 199.0 g. It is determined experimentally that it takes 16.0 J to raise the temperature 10.0°C. Find the specific heat of the object.
A) 8.04 J/kg ∙ K
B) 1600 J/kg ∙ K
C) 0.00120 J/kg ∙ K
D) 3.18 × 10

^{6}J/kg ∙ K Multiple Choice

Q 59

A 648-g empty iron kettle is put on a stove. How much heat. in joules. must it absorb to raise its temperature from 15.0°C to 37.0°C? (The specific heat for iron is 113 cal/kg•C°, 1 cal = 4.190 J)
A) 6740 J
B) 11,300 J
C) 1610 J
D) 16,100 J

Multiple Choice

Q 60

If we use 67 W of power to heat 148 g of water, how long will it take to raise the temperature of the water from 15°C to 25°C? The specific heat of water is 4190 J/kg•K.
A) 93 s
B) 5.3 s
C) 22 s
D) 114 h

Multiple Choice

Q 61

A 905-g meteor impacts the earth at a speed of 1629 m/s. If all of its energy is entirely converted to heat in the meteor, what will be the resulting temperature rise of the meteor, assuming it does not melt? The specific heat for the meteor material is 472 J/kg∙K, which is about the same as that of iron.
A) 2810°C
B) 2,540,000°C
C) 3.10°C
D) 11,700°C

Multiple Choice

Q 62

Heat is added to a pure substance in a closed container at a constant rate. The figure shows a graph of the temperature of the substance as a function of time. If L

_{f}= latent heat of fusion and L_{v}= latent heat of vaporization, what is the value of the ratio L_{v}/ L_{f}for this substance? A) 5.0 B) 4.5 C) 7.2 D) 3.5 E) 1.5 Multiple Choice

Q 63

A substance has a melting point of 20°C and a heat of fusion of 3.9 x 10

^{4}J/kg. The boiling point is 150°C and the heat of vaporization is 7.8 x 10^{4}J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg∙K), 1000 J/(kg∙K), and 400 J/(kg∙K), respectively. The quantity of heat required to raise the temperature of 3.80 kg of the substance from -61°C to 128°C, at a pressure of 1.0 atm, is closest to A) 620 kJ. B) 470 kJ. C) 560 kJ. D) 210 kJ. E) 770 kJ. Multiple Choice

Q 64

A substance has a melting point of 20°C and a heat of fusion of 3.5 × 10

^{4}J/kg. The boiling point is 150°C and the heat of vaporization is 7.0 × 10^{4}J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg∙K), 1000 J/(kg∙K), and 400 J/(kg∙K), respectively. The quantity of heat given up by 0.50 kg of the substance when it is cooled from 170°C to 88°C, at a pressure of 1.0 atmosphere, is closest to A) 70 kJ. B) 14 kJ. C) 21 kJ. D) 30 kJ. E) 44 kJ. Multiple Choice

Q 65

If 2.0 g of water at 0.00°C is to be vaporized, how much heat must be added to it? The specific heat of water is 1.0 cal/g∙K, its heat of fusion is 80 cal/g, and its heat of vaporization is 539 cal/g.
A) 1100 cal
B) 1100 kcal
C) 1200 cal
D) 1300 cal
E) 1500 cal

Multiple Choice

Q 66

If you add 700 kJ of heat to 700 g of water at 70.0°C, how much water is left in the container? The latent heat of vaporization of water is 2.26 × 10

^{6}J/kg and its specific heat is is 4190 J/(kg∙K). A) 429 g B) 258 g C) 340 g D) 600 g E) none Multiple Choice

Q 67

Heat is added to a 2.0 kg piece of ice at a rate of 793.0 kW. How long will it take for the ice to melt if it was initially at 0.00°C? (The latent heat of fusion for water is 334 kJ/kg and its latent heat of vaporization is 2260 kJ/kg.)
A) 0.84 s
B) 530,000 s
C) 4.7 s
D) 670 s

Multiple Choice

Q 68

A 406.0 kg copper bar is put into a smelter for melting. The initial temperature of the copper is 300.0 K. How much heat must the smelter produce to completely melt the copper bar? (The specific heat for copper is 386 J/kg•K, the heat of fusion for copper is 205 kJ/kg, and its melting point is 1357 K.)
A) 2.49 × 10

^{5}_{ kJ}B) 1.66 × 10^{11}_{ kJ}C) 1.66 × 10^{8}_{ kJ}D) 2.96 × 10^{5}_{ kJ} Multiple Choice

Q 69

A person pours 330 g of water at 45°C into an 855-g aluminum container with an initial temperature of 10°C. The specific heat of aluminum is 900 J/(kg∙K) and that of water is 4190 J/(kg∙K). What is the final temperature of the system, assuming no heat is exchanged with the surroundings?
A) 28°C
B) 32°C
C) 31°C
D) 33°C
E) 35°C

Multiple Choice

Q 70

A 400-g piece of metal at 120.0°C is dropped into a cup containing 450 g of water at 15.0°C. The final temperature of the system is measured to be 40.0°C. What is the specific heat of the metal, assuming no heat is exchanged with the surroundings or the cup? The specific heat of water is 4190 J/(kg∙K).
A) 1470 J/(kg ∙ K)
B) 2830 J/(kg ∙ K)
C) 3420 J/(kg ∙ K)
D) 3780 J/(kg ∙ K)
E) 4280 J/(kg ∙ K)

Multiple Choice

Q 71

An 80-g aluminum calorimeter contains 380 g of water at an equilibrium temperature of 20°C. A 120-g piece of metal, initially at 352°C, is added to the calorimeter. The final temperature at equilibrium is 32°C. Assume there is no external heat exchange. The specific heats of aluminum and water are 910 J/kg·K and 4190 J/kg·K, respectively. The specific heat of the metal is closest to
A) 520 J/kg ∙ K.
B) 480 J/kg ∙ K.
C) 390 J/kg ∙ K.
D) 350 J/kg ∙ K.
E) 560 J/kg ∙ K.

Multiple Choice

Q 72

Two experimental runs are performed to determine the calorimetric properties of an alcohol that has a melting point of -10°C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal equilibrium is 10°C. The specific heat of water is 4190 J/kg·K. Assume that no heat is exchanged with the styrofoam container and with the surroundings. The heat of fusion of the alcohol is closest to
A) 5.5 × 10

^{4}J/kg B) 6.3 × 10^{4}J/kg C) 7.1 × 10^{4}J/kg D) 7.9 × 10^{4}J/kg E) 8.7 × 10^{4}J/kg Multiple Choice

Q 73

Two experimental runs are performed to determine the calorimetric properties of an alcohol that has a melting point of -10°C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal equilibrium is 10°C. The specific heat of water is 4190 J/kg·K. Assume that no heat is exchanged with the styrofoam container and with the surroundings. The specific heat of the alcohol is closest to
A) 1700 J/kg·K.
B) 1900 J/kg·K.
C) 2100 J/kg·K.
D) 2300 J/kg·K.
E) 2500 J/kg·K.

Multiple Choice

Q 74

A person makes ice tea by adding ice to 1.8 kg of hot tea, initially at 80°C. How many kilograms of ice, initially at 0.00°C, are required to bring the mixture to 10°C? The heat of fusion of ice is 334 kJ/kg, and we can assume that tea has essentially the same thermal properties as water, so its specific heat is 4190 J/(kg∙K).
A) 1.0 kg
B) 1.2 kg
C) 1.4 kg
D) 1.5 kg
E) 1.7 kg

Multiple Choice

Q 75

A block of ice at 0.000°C is added to a well-insulated 147-g aluminum calorimeter cup that holds 200 g of water at 10.0°C. The water and aluminum cup are in thermal equilibrium, and the specific heat of aluminum is 910 J/(kg∙K). If all but 2.00 g of ice melt, what was the original mass of the block of ice? The specific heat of water is 4190 J/(kg∙K), its latent heat of fusion is 334 kJ/kg, and its latent heat of vaporization is 2260 kJ/kg.
A) 31.1 g
B) 35.6 g
C) 38.8 g
D) 42.0 g
E) 47.6 g

Multiple Choice

Q 76

A copper cylinder with a mass of 125 g and temperature of 345°C is cooled by dropping it into a glass beaker containing 565 g of water initially at 20.0°C. The mass of the beaker is 50.0 g and the specific heat of the glass is 840 J/kg∙K. What is the final equilibrium temperature of the system, assuming the cooling takes place very quickly, so that no energy is lost to the air? The specific heat of copper is 385 J/kg∙K and that of water is 4190 J/kg∙K.

Short Answer

Q 77

A 200-g metal container, insulated on the outside, holds 100 g of water in thermal equilibrium at 22.00°C. A 21-g ice cube, at the melting point, is dropped into the water, and when thermal equilibrium is reached the temperature is 15.00°C. Assume there is no heat exchange with the surroundings. For water, the specific heat is 4190 J/kg · K and the heat of fusion is 3.34 × 10

^{5}J/kg. The specific heat for the metal is closest to A) 3850 J/kg ∙ K. B) 2730 J/kg ∙ K. C) 4450 J/kg ∙ K. D) 4950 J/kg ∙ K. E) 5450 J/kg ∙ K. Multiple Choice

Q 78

How many grams of ice at -13°C must be added to 711 grams of water that is initially at a temperature of 87°C to produce water at a final temperature of 10.0°C? Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is 4190 J/kg·C° and of ice is 2050 J/kg·C°. For water the normal melting point is 0.00°C and the heat of fusion is 334 × 10

^{3}J/kg. The normal boiling point is 100°C and the heat of vaporization is 2.26 × 10^{6}J/kg. Short Answer

Q 79

What is the steady state rate of heat flow through a pane of glass that is 40.0 cm by 30.0 cm with a thickness of 4.00 mm when the outside temperature of the glass is -10.0°C and its inside temperature is 25.0°C? The thermal conductivity of glass is 0.105 W/(m∙K), the specific heat of glass is 0.180 cal/(g∙°C), and 1 cal = 4.190 J.
A) 24.2 W
B) 3.81 W
C) 18.6 W
D) 47.3 W
E) 110 W

Multiple Choice

Q 80

Under steady state conditions, a piece of wood 350 mm by 350 mm and 15 mm thick conducts heat through its thickness and loses no appreciable heat through its well-insulated sides. The rate of heat flow is measured to be 14.0 W when the temperature difference across its thickness is 28 C°. Determine the thermal conductivity of this wood.
A) 9.2 × 10

^{-4}W/(m∙C°) B) 270 W/(m∙C°) C) 16 W/(m∙C°) D) 0.061 W/(m∙C°) E) 33 W/(m∙C°) Multiple Choice

Q 81

A solid concrete wall 4.0 m by 2.4 m and 30 cm thick, with a thermal conductivity of 1.3 W/(m∙K), separates a basement at 18°C from the ground outside at 6°C. Under steady state conditions, how much heat flows through the wall in one hour?
A) 1.8 MJ
B) 1.8 kJ
C) 500 J
D) 5.0 MJ
E) 5.0 kJ

Multiple Choice

Q 82

Two metal rods, one silver and the other copper, are both attached to a steam chamber as shown in the figure, with a temperature of 100°C, at one end, and an ice water bath, with a temperature of 0°C, at the other. The rods are 5.0 cm long and have a square cross-section, 2.0 cm on a side. When steady state has been reached, how much heat flows through the two rods in 1.0 min? The thermal conductivity of silver is 417 W/(m∙K), and that of copper is 395 W/(m∙K). No heat is exchanged between the rods and the surroundings, except at their ends.
A) 20 kJ
B) 39 kJ
C) 47 kJ
D) 49 kJ
E) 11 kJ

Multiple Choice

Q 83

A heat conducting rod, 0.90 m long, is made of an aluminum section that is 0.10 m long, and a copper section that is 0.80 m long. Both sections have cross-sectional areas of 0.00040 m

^{2}. The aluminum end is maintained at a temperature of 40°C and the copper end is at 150°. The thermal conductivity of aluminum is 205 W/m∙K and of copper is 385 W/m∙K. Steady state has been reached, and no heat is lost through the well-insulated sides of the rod. The temperature of the aluminum-copper junction in the rod is closest to A) 61°C. B) 58°C. C) 56°C. D) 54°C. E) 52°C. Multiple Choice

Q 84

A heat conducting rod, 1.40 m long, is made of an aluminum section that is 0.50 m long and a copper section that is 0.90 m long. Both sections have cross-sectional areas of of 0.00040 m

^{2}. The aluminum end and the copper end are maintained at temperatures of 40°C and 280°C, respectively. The thermal conductivity of aluminum is 205 W/m∙K of copper is 385 W/m∙K. The rate at which heat is conducted in the rod is closest to A) 20 W. B) 18 W. C) 23 W. D) 25 W. E) 28 W. Multiple Choice

Q 85

Some properties of glass are listed here.
Density: 2300 kg/m

^{3}Specific heat: 840 J/kg·C° Coefficient of linear thermal expansion: 8.5 × 10^{-6}(C°)^{-1}Thermal conductivity: 0.80 W/(m·C°) A glass window pane is 2.7 m high, 2.4 m wide, and 2.0 mm thick. The temperature at the inner surface of the glass is 22°C and at the outer surface 4.0°C. How much heat is lost each hour through the window under steady state conditions? A) 1.7 × 10^{8 J}B) 1.7 × 10^{5 J}C) 4.7 × 10^{4 J}D) 4.7 × 10^{1 J}E) 1.7 × 10^{6 J} Multiple Choice

Q 86

A cylindrical bar that us well insulated around its sides connects hot and cold reservoirs and conducts heat at a rate of 10.0 J/s under steady state conditions. If all of its linear dimensions (diameter and length) are reduced by half, the rate at which it will now conduct heat between the same reservoirs is closest to
A) 80.0 J/s.
B) 20.0 J/s.
C) 5.00 J/s.
D) 2.50 J/s.
E) 1.25 J/s.

Multiple Choice

Q 87

A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The room temperature is maintained at -10°C and the outside temperature is 20°C The inside wall is to be covered by a layer of wood in order to reduce the rate of heat loss through the wall BY 90 percent. The thermal conductivities of concrete and wood are 0.80 W/m·K and 0.040 W/m·K, respectively. Under steady state conditions, the thickness of the layer of wood required is closest to
A) 60 mm.
B) 70 mm.
C) 80 mm.
D) 90 mm.
E) 100 mm.

Multiple Choice

Q 88

The walls of an ice chest are made of 2.00-mm-thick insulation having a thermal conductivity 0.00300 W/m∙K. The total surface area of the ice chest is 1.20 m

^{2}. If 4.00 kg of ice at 0.00°C are placed in the chest and the temperature of the outside surface of the chest is 20.0°C, how long does it take the ice to melt under steady state conditions? The latent heat of fusion of water is 79.6 cal/g = 334 kJ/kg. A) 4.22 h B) 22.1 h C) 17.6 h D) 1.33 d E) 10.3 h Multiple Choice

Q 89

A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water 100°C and the other end in a water-ice mixture at 0.00°C. The rod has uniform cross-sectional area of 4.04 cm

^{2}and length of 91 cm. Under steady state conditions, the heat conducted by the rod melts the ice at a rate of 1.0 g every 34 seconds. What is the thermal conductivity of the rod? (The heat of fusion of water is Short Answer

Q 90

A spherical object 25.0 cm in diameter having an emissivity of 0.800 is held at a temperature of 275°C by an internal heater. This object is embedded in a very large vat of water at 100.0°C and atmospheric pressure. At what maximum rate (in g/min) is the water evaporating in the vat due to the radiated heat it receives from the object? You can ignore any heat radiated by the water. The latent heat of fusion for water is 33,400 J/kg, its latent heat of vaporization is 2.26 × 10

^{6}J/kg, and the Stefan-Boltzmann constant is 5.670 × 10^{-8}W/m^{2}· K^{4}. Short Answer

Q 91

The filament in a light bulb has a diameter of 0.050 mm and an emissivity of 1.0. The temperature of the filament is 3000°C. What should be the length of the filament so it will radiate 60 W of power? The Stefan-Boltzmann constant is 5.670 × 10

^{-8}W/m^{2}· K^{4}. A) 11 cm B) 9.4 cm C) 8.6 cm D) 7.2 cm E) 5.9 cm Multiple Choice

Q 92

A blacksmith is flattening a steel plate that measures 10 cm × 15 cm × 1 mm. He has heated the plate to 900 K. If the emissivity of the plate is 0.75, what is the total rate at which it radiates energy? The Stefan-Boltzmann constant is 5.670 × 10

^{-8}W/m^{2}· K^{4}. Ignore any heat it receives from the surroundings. A) 360 W B) 760 W C) 790 W D) 850 W E) 880 W Multiple Choice

Q 93

Betelgeuse is a red supergiant star in the constellation Orion. It radiates heat at the rate of 2.70 × 10

^{30}W and has a surface temperature of 3000 K. Assuming that it is a perfect emitter, what is the radius of Betelgeuse? The Stefan-Boltzmann constant is 5.670 × 10^{-8}W/m^{2}· K^{4}. A) 7.80 × 10^{10}m B) 8.70 × 10^{10}m C) 1.40 × 10^{11}m D) 1.90 × 10^{11}m E) 2.16 × 10^{11}m Multiple Choice

Q 94

A cube at 100.0°C radiates heat at a rate of 80.0 J/s. If the length of each side is cut in half, the rate at which it will now radiate is closest to
A) 56.6 J/s.
B) 40.0 J/s.
C) 28.3 J/s.
D) 20.0 J/s.
E) 10.0 J/s.

Multiple Choice

Q 95

A cube at 100°C radiates heat at a rate of 80.0 J/s. If its surface temperature is increased to 200°C, the rate at which it will now radiate is closest to
A) 160 J/s.
B) 207 J/s.
C) 320 J/s.
D) 640 J/s.
E) 1280 J/s.

Multiple Choice

Q 96

What is the net power that a person loses through radiation if her surface area is 1.20 m

^{2}, if her emissivity is 0.895, if her skin temperature is 300 K, and if she is in a room that is at a temperature of 17°C? The Stefan-Boltzmann constant is 5.670 × 10^{-8}W/m^{2}· K^{4}. A) 60.3 W B) 62.6 W C) 65.7 W D) 68.4 W E) 64.8 W Multiple Choice

Q 97

A solid metal sphere is 15.0 cm in diameter and has surface of uniform color. When its surface is at 112°C, you measure that it radiates energy at a rate of 71.3 W. What is the emissivity of the surface of this object? Any heat that enters the sphere from the outside environment is negligible. The Stefan-Boltzmann constant is 5.670 × 10

^{-8}W/m^{2}· K^{4}. Short Answer

Q 98

A radiating body originally has a Kelvin temperature T

_{o}, and its surroundings are at 500K (T_{o }> 500K). If the Kelvin temperature of the radiating body is increased to 3T_{o}, the net rate at which the body radiates increases by a factor of 333. What was the original temperature T_{o}? Short Answer