Deck 14: Heat

Question 1

Choose the one alternative that best completes the statement or answers the question.
Object 1 has three times the specific heat capacity and four times the mass of Object 2 . The two objects are heated from the same initial temperature, $T _ { 0 }$ to the same final temperature $T _ { \mathbf { f } }$ During this process, if Object 1 absorbs heat Q , the amount of heat absorbed by Object 2 will be

A) $12 Q$
B) $\frac { 3 } { 4 } Q .$
C) $6 Q$
D) $\frac { 1 } { 12 } Q$
E) $\frac { 4 } { 3 } Q .$

Answer 1

D

Question 2

Choose the one alternative that best completes the statement or answers the question.
Two metal rods are to be used to conduct heat from a region at $100 ^ { \circ } \mathrm { C }$ to a region at $0 ^ { \circ } \mathrm { C }$ as shown in the figure. The rods can be placed in parallel, as shown on the left, or in series, as on the right. When steady state flow is established, the heat conducted in the series arrangement is

A) the same as the heat conducted with the rods in parallel.
B) Iess than the heat conducted with the rods in parallel.
C) greater than the heat conducted with the rods in parallel.

Answer 2

B

Question 3

Choose the one alternative that best completes the statement or answers the question.
A 5.00-g lead BB moving at 44.0 m/s penetrates a wood block and comes to rest inside the block. If half of its kinetic energy is absorbed by the BB, what is the change in the temperature of the BB? The specific heat of lead is 128 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } .$

A) 2.78 K
B) 3.78 K
C) 1.10 K
D) 1.26 K
E) 0.940 K

Answer 3

B

Question 4

Choose the one alternative that best completes the statement or answers the question.
A 920-g empty iron kettle is put on a stove. How much heat in joules must it absorb to raise its temperature form $15.0 ^ { \circ } \mathrm { C } \text { to } 93.0 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat for iron is $113 \mathrm { cal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ and 1 cal=4.186 J

A) 40,500 J
B) 40,100J
C) 33,900 J
D) 8110 J

Question 5

Choose the one alternative that best completes the statement or answers the question.
The figure shows a graph of the temperature of a pure substance as a function of time as heat is added to it at a constant rate in a closed container. If $L F$ is the latent heat of fusion of this substance and $L V$ is its latent heat of vaporization, what is the value of the ratio $L V / L F ?$

A) 4.5
B) 7.2
C) 1.5
D) 3.5
E) 5.0

Question 6

Choose the one alternative that best completes the statement or answers the question.
On his honeymoon, James Joule attempted to explore the relationships between various forms of energy by measuring the rise of temperature of water which had fallen down a waterfall on Mount Blanc. What maximum temperature rise would one expect for a waterfall with a vertical drop of 20 m? The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A) $0.064 \mathrm { C } ^ { \circ }$
B) $0.047 \mathrm { C } ^ { \circ }$
C) $0.071 \mathrm { C } ^ { \circ }$
D) $0.053 \mathrm { C } ^ { \circ }$

Question 7

Choose the one alternative that best completes the statement or answers the question.
A glass beaker of unknown mass contains 74.0 ml of water. The system absorbs 2000.0 cal of heat and the temperature rises $20.0 ^ { \circ } \mathrm { C }$ as a result. What is the mass of the beaker? The specific heat of glass is $0.18 \mathrm { cal } / \mathrm { g } \cdot { } ^ { \circ } \mathrm { C }$ and that of water is $1.0 \mathrm { cal } / \mathrm { g } \cdot \mathrm { C } ^ { \circ }$

A) 560 g
B) 540 g
C) 140 g
D) 270,000 g

Question 8

Choose the one alternative that best completes the statement or answers the question.
Object 1 has three times the specific heat capacity and four times the mass of Object 2. The two objects are given the same amount of heat. If the temperature of Object 1 changes by an amount $\Delta T$ the change in temperature of Object 2 will be

A) $\frac { 3 } { 4 } \Delta \mathrm { T }$
B) $\frac { 4 } { 3 } \Delta T \text {. }$
C) $12 \Delta T$
D) $\Delta T$
E) $6 \Delta T \text {. }$

Question 9

Choose the one alternative that best completes the statement or answers the question.
An aluminum electric tea kettle with a mass of 500 g is heated with a 500 -W heating coil. How Iong will it take to heat up 1.0 kg of water from $18 ^ { \circ } \mathrm { C } \text { to } 98 ^ { \circ } \mathrm { C }$ in the tea kettle? The specific heat of aluminum is 900 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ and that of water is 4186 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } .$

A) 18 minutes
B) 15 minutes
C) 12 minutes
D) 7.0 minutes
E) 5.0 minutes

Question 10

Choose the one alternative that best completes the statement or answers the question.
If 150 kcal of heat raises the temperature of 2.0 kg of a material by 400 F°, what is the specific heat capacity of the material?

A) $0.75 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$
B) $0.34 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$
C) $0.19 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$
D) $1.35 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$

Question 11

Choose the one alternative that best completes the statement or answers the question.
A 6.5-g iron meteor hits the earth at a speed of 295 m/s. If its kinetic energy is entirely converted to heat in the meteor, by how much will its temperature rise? The specific heat of iron is $113 \mathrm { cal } / \mathrm { kg } \text {. }$ $\mathrm { C } ^ { \circ }$ and 1 cal=4.186 J

A) $57,100 \mathrm { C } ^ { \circ }$
B) $92.0 \mathrm { C } ^ { \circ }$
C) $384 C ^ { \circ }$
D) $0.147 \mathrm { C } ^ { \circ }$

Question 12

Choose the one alternative that best completes the statement or answers the question.
It is necessary to determine the specific heat of an unknown object. The mass of the object is 201.0 g. It is determined experimentally that it takes 15.0 J to raise the temperature $10.0 ^ { \circ } \mathrm { C }$ What isthe specific heat of the object?

A) $0.00130 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
B) $7.46 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
C) $3,020,000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
D) $1500 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

Question 13

Choose the one alternative that best completes the statement or answers the question.
The water flowing over Niagara Falls drops a distance of 50 m. If all the gravitational potential energy is converted to thermal energy, by what temperature does the water rise? The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A) $0.42 \mathrm { C } ^ { \circ }$
B) $0.37 \mathrm { C } ^ { \circ }$
C) $0.10 \mathrm { C } ^ { \circ }$
D) $0.12 \mathrm { C } ^ { \circ }$

Question 14

Choose the one alternative that best completes the statement or answers the question.
In grinding a steel knife, the metal can get as hot as $400 ^ { \circ } \mathrm { C }$ If the blade has a mass of 80 g, what is the minimum amount of water needed at $20 ^ { \circ } \mathrm { C }$ if the water is to remain liquid and not rise above $100 ^ { \circ } \mathrm { C }$ when the hot blade is quenched in it? The specific heat of the steel is $0.11 \mathrm { cal } / \mathrm { g } \cdot \mathrm { C } ^ { \circ }$ and the specific heat of water is $1.0 \mathrm { cal } / \mathrm { g } \cdot \mathrm { C } ^ { \circ }$

A) 55 g
B) 22 g
C) 44 g
D) 33 g

Question 15

Choose the one alternative that best completes the statement or answers the question.
How much heat must be removed from 456 g of water at $25.0 ^ { \circ } \mathrm { C }$ to change it into ice at $- 10.0 ^ { \circ } \mathrm { C } ?$ The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ and the specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A) 153 kJ
B) 210 kJ
C) 57.3 kJ
D) 47.7 kJ
E) 105 kJ

Question 16

Choose the one alternative that best completes the statement or answers the question.
In a flask, 114.0 g of water is heated using 67.0 W of power, with perfect efficiency. How long will it take to raise the temperature of the water from $15 ^ { \circ } \mathrm { C } \text { to } 25 ^ { \circ } \mathrm { C } ?$ The specific heat of water is 4186 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } .$

A) 17 s
B) 71 s
C) 320,000 s
D) 4.1 s

Question 17

Choose the one alternative that best completes the statement or answers the question.
A container of 114.0 g of water is heated using 67.0 W of power, with perfect efficiency. How long will it take to raise the temperature of the water from $15 ^ { \circ } \mathrm { C } \text { to } 25 ^ { \circ } \mathrm { C } \text { ? }$
The specific heat capacity of the container is negligible, and the specific heat capacity of water is $4.186 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C }$

A) 320,000 s
B) 17 s
C) 71 s
D) 4.1 s

Question 18

Choose the one alternative that best completes the statement or answers the question.
A machine part consists of 0.10 kg of iron (of specific heat 470 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ ) and 0.16 kg of copper (of specific heat 390 $\mathrm { J } / \mathrm { Kg } \cdot \mathrm { K } )$ How much heat must be added to the gear to raise its temperature from $18 ^ { \circ } \mathrm { C } \text { to } 53 ^ { \circ } \mathrm { C } ?$

A) 910 J
B) 4000 J
C) 3800 J
D) 4400 J

Question 19

Choose the one alternative that best completes the statement or answers the question.
A 200-L electric water heater uses 2.0 kW. Assuming no heat loss, how many hours would it take to heat the water in this tank from $23 ^ { \circ } \mathrm { C } \text { to } 75 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and its density is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 6.0 hours
B) 5.0 . hours
C) 7.0 hours
D) 8.0 hours

Question 20

Choose the one alternative that best completes the statement or answers the question.
A carpenter is driving a 15.0-g steel nail into a board. His 1.00-kg hammer is moving at 8.50 m/s when it strikes the nail. Half of the kinetic energy of the hammer is transformed into heat in the nail and does not flow out of the nail. What is the increase in temperature of the nail after the three blows that the carpenter needs to drive the nail in completely? The specific heat of steel is 448 J/kg . K

A) 2.7 K
B) 8.1 K
C) 3.6 K
D) 7.7 K
E) 1.8 K

Question 21

Choose the one alternative that best completes the statement or answers the question.
A substance has a melting point of $20 ^ { \circ } \mathrm { C }$ and a heat of fusion of $3.6 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $7.2 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ at a pressure of one atmosphere. The specific heats for the solid, liquid, and gaseous phases are $600 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (solid), } 1000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (liquid), and } 400$ $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } \text { (gaseous). }$ How much heat is given up by 2.80 kg of this substance when it is cooled from $170 ^ { \circ } \mathrm { C } \text { to } 86 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

A) 640 kJ
B) 300 kJ
C) 200 kJ
D) 400 kJ
E) 440 kJ

Question 22

Choose the one alternative that best completes the statement or answers the question.
If 50 g of lead (of specific heat $\left. 0.11 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \right)$ at $100 ^ { \circ } \mathrm { C }$ is put into 75 g of water (of specific heat $\left. 1.0 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \right) \text { at } 0 ^ { \circ } \mathrm { C }$ What is the final temperature of the mixture?

A) $50 ^ { \circ } \mathrm { C }$
B) $25 ^ { \circ } \mathrm { C }$
C) $2.0 ^ { \circ } \mathrm { C }$
D) $6.8 ^ { \circ } \mathrm { C }$

Question 23

Choose the one alternative that best completes the statement or answers the question.
How much heat must be added to a 8.0 -kg block of ice at $- 8 ^ { \circ } \mathrm { C }$ to change it to water at $14 ^ { \circ } \mathrm { C } ?$ The
specific heat of ice is $2050 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ the specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ the latent heat of fusion of ice is 334,000 J/kg, and 1cal=4.186 J.

A) 730 kcal
B) 780 kcal
C) 140 kcal
D) 810 kcal
E) 180 kcal

Question 24

Write the word or phrase that best completes each statement or answers the question.
A beaker of negligible heat capacity contains 456 g of ice at $- 25.0 ^ { \circ } \mathrm { C }$ A lab technician
begins to supply heat to the container at the rate of 1000 J/min . How long after starting will
it take before the temperature starts to rise above $0 ^ { \circ } \mathrm { C } ?$ The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } .$ $\mathrm { K }$ and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

Question 25

Choose the one alternative that best completes the statement or answers the question.
A substance has a melting point of $20 ^ { \circ } \mathrm { C }$ and a heat of fusion of $3.4 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $6.8 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ at a pressure of one atmosphere. The specific heats for the solid, liquid, and gaseous phases are 600 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } \text { (solid), } 1000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (liquid), }$ and 400 $\text { J/kg } \cdot K \text { (gaseous). }$ How much heat is required to raise the temperature of 1.90 kg of this substance from $- 4 ^ { \circ } \mathrm { C } \text { to } 106 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

A) 320 kJ
B) 260 kJ
C) 190 kJ
D) 230 kJ
E) 92 kJ

Question 26

Write the word or phrase that best completes each statement or answers the question.
A beaker of negligible heat capacity contains 456 g of ice at $- 25.0 ^ { \circ } \mathrm { C }$ A lab technician begins to supply heat to the container at the rate of 1000 J/min. How long after starting will the ice begin to melt, assuming all of the ice has the same temperature? The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

Question 27

Choose the one alternative that best completes the statement or answers the question.
A 45.0-kg sample of ice is at $0.00 ^ { \circ } \mathrm { C }$ How much heat is needed to melt it? For water $L F = 334,000$ $\mathrm { J } / \mathrm { kg } \text { and } L V = 2.256 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg } \text {. }$

A) $4.10 \times 10 ^ { 6 } \mathrm {~kJ}$
B) $1.50 \times 10 ^ { 4 } \mathrm {~kJ}$
C) 0.00 kJ
D) $1.02 \times 10 ^ { 5 } \mathrm {~kJ}$

Question 28

Choose the one alternative that best completes the statement or answers the question.
The melting point of aluminum is $660 ^ { \circ } \mathrm { C }$ its latent heat of fusion is $4.00 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ and its specific heat is $900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ How much heat must be added to 500 g of aluminum at $27 ^ { \circ } \mathrm { C }$ to completely melt it?

A) 273 kJ
B) 14 kJ
C) 395 kJ
D) 485 kJ
E) 147 kJ

Question 29

Choose the one alternative that best completes the statement or answers the question.
A .20-kg ice cube at $0.0 ^ { \circ } \mathrm { C }$ has sufficient heat added to it to cause total melting, and the resulting water is heated to $70.0 ^ { \circ } \mathrm { C }$ How much heat is added? For water $L _ { F } = 334,000 \mathrm {~J} / \mathrm { kg } , L \mathrm {~V} = 2.256 \times 10 ^ { 6 }$ $\mathrm { J } / \mathrm { kq } _ { \text {, the } c } = 4.186 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { kq } \cdot \mathrm { C } \text {. }$

A) 81 kJ
B) 59 kJ
C) 130 kJ
D) 14,000 kJ

Question 30

Choose the one alternative that best completes the statement or answers the question.
A 2294-kg sample of water at $0 ^ { \circ } \mathrm { C }$ is cooled to $- 36 ^ { \circ } \mathrm { C }$ and freezes in the process. How much heat is liberated? For water $L F = 334,000 \mathrm {~J} / \mathrm { kg } \text { and } L V = 2.256 \times 10^6 \mathrm {~J} / \mathrm { kg }$ The specific heat of ice is 2050 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$

A) 935,000 kJ
B) 334,000 kJ
C) 597,000 kJ
D) 1,110,000 kJ

Question 31

Choose the one alternative that best completes the statement or answers the question.
A lab assistant pours 330 g of water at $45 ^ { \circ } \mathrm { C }$ into an 855-g aluminum container that is at an initial temperature of $10 ^ { \circ } \mathrm { C }$ The specific heat of aluminum is $900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ What is the final temperature of the system, assuming no heat is exchanged with the surroundings?

A) $32 ^ { \circ } \mathrm { C }$
B) $35 ^ { \circ } \mathrm { C }$
C) $28 ^ { \circ } \mathrm { C }$
D) $31 ^ { \circ } \mathrm { C }$
E) $33 ^ { \circ } \mathrm { C }$

Question 32

Choose the one alternative that best completes the statement or answers the question.
A 771.0-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 $386 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ the heat of fusion for copper is 205,000 J/kg, and its melting point is 1357 K.

A) $4.73 \times 10 ^ { 5 } \mathrm {~kJ}$
B) $3.15 \times 10 ^ { 8 } \mathrm {~kJ}$
C) $3.15 \times 10 ^ { 11 } \mathrm {~kJ}$
D) $5.62 \times 10 ^ { 5 } \mathrm {~kJ}$

Question 33

Choose the one alternative that best completes the statement or answers the question.
A metal has a latent heat of fusion of $2.32 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg } _ { 1 }$ a specific heat of $128 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } _ { \mathrm { r } }$ and a melting point of $228 ^ { \circ } \mathrm { C } \text {. }$ A 30-g pellet of this metal at $16 ^ { \circ } \mathrm { C }$ hits a solid wall and comes to a complete stop. What would the speed of the pellet have to be in order for it to melt completely when it hits the wall, assuming that all of its kinetic energy is transformed into heat within the pellet?

A) 317 m/s
B) 232 m/s
C) 215 m/s
D) 273 m/s
E) 207 m/s

Question 34

Choose the one alternative that best completes the statement or answers the question.
If you add 700 kJ of heat to 700 g of water originally at $70.0 ^ { \circ } \mathrm { C }$ how much water is left in the container? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ and its specific heat capacity is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$

A) 258 g
B) 340 g
C) 600 g
D) 429 g
E) none

Question 35

Choose the one alternative that best completes the statement or answers the question.
Heat is added to a 3.0 kg piece of ice at a rate of 636.0 kW. How long will it take for the ice at $0.0 ^ { \circ } \mathrm { C }$ to melt? For water $L F = 334,000 \mathrm {~J} / \mathrm { kg } \text { and } L V = 2.246 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg }$

A) 1000 s
B) 640,000 s
C) 1.6 s
D) 0.0 s

Question 36

Choose the one alternative that best completes the statement or answers the question.
Solar houses use a variety of energy storage devices to retain the heat absorbed during the day so
that it can be released during the night. Suppose that you were to use a device of this kind to
produce steam at $100 ^ { \circ } \mathrm { C }$ during the day, and then allow the steam to cool to $0 ^ { \circ } \mathrm { C }$ and freeze during
the night. How many kilograms of water would be needed to store 20.0 kWh of energy in this
way? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ and the specific heat capacity of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A) 42.6 kg
B) 54.2 kg
C) 23.9 kg
D) 12.4 kg
E) 35.7 kg

Question 37

Choose the one alternative that best completes the statement or answers the question.
A person tries to heat up her bath water by adding 5.0 L of water at $80 ^ { \circ } \mathrm { C }$ to 60 L of water at $30 ^ { \circ } \mathrm { C }$ What is the final temperature of the bath water?

A) $36 ^ { \circ } \mathrm { C }$
B) $40 ^ { \circ } \mathrm { C }$
C) $34 ^ { \circ } \mathrm { C }$
D) $38 ^ { \circ } \mathrm { C }$

Question 38

Choose the one alternative that best completes the statement or answers the question.
If you add 1.33 MJ of heat to 500 g of water at $50 ^ { \circ } \mathrm { C }$ in a sealed container, what is the final temperature of the steam? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ heat of steam is $2010 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } _ { 1 }$ and the specific heat of water is $4186 \mathrm {~J} / \mathrm { kq } \cdot \mathrm { K }$ the specific

A) $147 ^ { \circ } \mathrm { C }$
B) $112 ^ { \circ } \mathrm { C }$
C) $100 ^ { \circ } \mathrm { C }$
D) $195 ^ { \circ } \mathrm { C }$
E) $123 ^ { \circ } \mathrm { C }$

Question 39

Write the word or phrase that best completes each statement or answers the question.
The melting point of aluminum is $660 ^ { \circ } \mathrm { C }$ its latent heat of fusion is $4.00 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ and its specific heat is $900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ If 300 kJ of heat are added to 442 g of aluminum at $100 ^ { \circ } \mathrm { C }$
what is the final state of the system? That is, how much is liquid, how much is solid, and
what is its temperature?

Question 40

Choose the one alternative that best completes the statement or answers the question.
A runner generates 1260 W of thermal energy. If this heat has to be removed only by evaporation, how much water does this runner lose in 15 minutes of running? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$

A) 350 g
B) 35 g
C) 50 g
D) 40 g
E) 500 g

Question 41

Choose the one alternative that best completes the statement or answers the question.
A 40.0-g block of ice at - $15.00 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter (of negligible heat capacity) containing water at $15.00 ^ { \circ } \mathrm { C }$ When equilibrium is reached, the final temperature is $8.00 ^ { \circ } \mathrm { C }$ How much water did the calorimeter contain initially? The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

A) 302 g
B) 546 g
C) 634 g
D) 405 g
E) 345 g

Question 42

Choose the one alternative that best completes the statement or answers the question.
A lab student drops a 400.0-g piece of metal at $120.0 ^ { \circ } \mathrm { C }$ into a cup containing 450.0 g of water at $15.0 ^ { \circ } \mathrm { C }$ After waiting for a few minutes, the student measures that the final temperature of the system is $40.0 ^ { \circ } \mathrm { C }$ What is the specific heat of the metal, assuming that no significant heat is exchanged with the surroundings or the cup? The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$

A) $2830 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
B) $1470 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
C) $4280 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
D) $3780 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
E) $3420 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

Question 43

Choose the one alternative that best completes the statement or answers the question.
11A 90-g aluminum calorimeter contains 390 g of water at an equilibrium temperature of $20 ^ { \circ } \mathrm { C }$ A 160-g piece of metal, initially at $305 ^ { \circ } \mathrm { C }$ is added to the calorimeter. The final temperature at equilibrium is $32 ^ { \circ } \mathrm { C }$ Assume there is no external heat exchange. The specific heat capacities of aluminum and water are 910 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ (aluminum) and 4190 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ (water). What is the specific heat capacity of the 160-\mathrm{g} piece of metal?

A) $470 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
B) $510 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
C) $430 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
D) $310 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
E) $350 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

Question 44

Choose the one alternative that best completes the statement or answers the question.
A 35-g block of ice at - $14 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter (of negligible heat capacity) containing 400 g of water at $0 ^ { \circ } \mathrm { C }$ When the system reaches equilibrium, how much ice is left in the calorimeter? The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

A) 38 g
B) 41 g
C) 35 g
D) 33 g
E) 32 g

Question 45

Choose the one alternative that best completes the statement or answers the question.
An 920-g piece of iron at $100 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter of negligible heat capacity containing 50 g of ice at $0 ^ { \circ } \mathrm { C }$ and 92 g of water, also at $0 ^ { \circ } \mathrm { C }$ What is the final temperature of the system? The specific heat of iron is 448 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ that of water is 4186 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } _ { 1 }$ , and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

A) $32 ^ { \circ } \mathrm { C }$
B) $0 ^ { \circ } \mathrm { C }$
C) $11 ^ { \circ } \mathrm { C }$
D) $24 ^ { \circ } \mathrm { C }$
E) $14 ^ { \circ } \mathrm { C }$

Question 46

Choose the one alternative that best completes the statement or answers the question.
A person is walking outdoors on a cold day when the temperature is $- 20 ^ { \circ } \mathrm { C }$ He is breathing at the rate of 16 breaths per minute, and each time he breathes in he inhales $0.0050 m ^ { 3 }$ of air. At what rate does he lose heat from breathing if the air in his lungs is heated to body temperature $\left( 37 ^ { \circ } \mathrm { C } \right)$ before it is exhaled? The specific heat of air is $1020 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the density of air is $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 300 W
B) 150 W
C) 60 W
D) 90 W
E) 100 W

Question 47

Choose the one alternative that best completes the statement or answers the question.
A 0.600-kg piece of metal X is heated to $100 ^ { \circ } \mathrm { C }$ and placed in an aluminum can of mass 0.200-kg
which contains $0.500 \mathrm {~kg}$ of water initially at $17.3 ^ { \circ } \mathrm { C }$ The final equilibrium temperature of the mixture is $20.2 ^ { \circ } \mathrm { C }$ What is the specific heat of metal X? The specific heats of water and aluminum are 4186 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ (water) and 910 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } \text { (aluminum). }$

A) $140 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
B) $450 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
C) $900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
D) $270 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

Question 48

Choose the one alternative that best completes the statement or answers the question.
Two experimental runs are performed to determine the calorimetric properties of an alcohol which
has a melting point of $- 10.0 ^ { \circ } \mathrm { C } .$ In the first run, a 200-g cube of frozen alcohol, at the melting point,
is added to 300 g of water at $20.0 ^ { \circ } \mathrm { C }$ in a styrofoam container. When thermal equilibrium is
reached, the alcohol-water solution is at a temperature of $5.0 ^ { \circ } \mathrm { C }$ In the second run, an identical
cube of alcohol is added to 500 g of water at $20.0 ^ { \circ } \mathrm { C }$ and the temperature at thermal equilibrium is
$10.0 ^ { \circ } \mathrm { C }$ The specific heat capacity of water is $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$ Assume no heat is exchanged with the
styrofoam container and the surroundings. What is the heat of fusion of the alcohol?

A) $8.7 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$
B) $7.9 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$
C) $7.1 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$
D) $6.3 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$
E) $5.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

Question 49

Write the word or phrase that best completes each statement or answers the question.
A 600-g piece of iron at $100 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter of negligible heat capacity
containing 100 g of ice at $0 ^ { \circ } \mathrm { C }$ and 120 g of water, also at $0 ^ { \circ } \mathrm { C }$ What is the final temperature
of the system? The specific heat of iron is $448 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ the latent heat of fusion of water is
$33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ and the specific heat of water is $4186 \mathrm {~J} / \mathrm { kq } \cdot \mathrm { K }$

Question 50

Choose the one alternative that best completes the statement or answers the question.
Two experimental runs are performed to determine the calorimetric properties of an alcohol which has a melting point of $- 10 ^ { \circ } \mathrm { C }$ In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at $20 ^ { \circ } \mathrm { C }$ in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of $5 ^ { \circ } \mathrm { C }$ In the second run, an identical cube of alcohol is added to 500 g of water at $20 ^ { \circ } \mathrm { C }$ and the temperature at thermal equilibrium is $10 ^ { \circ } \mathrm { C }$ specific heat capacity of water is $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
Assume no heat is exchanged with the styrofoam container and the surroundings. What is the specific heat capacity of the alcohol?

A) $1700 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
B) $2500 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
C) $2100 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
D) $2300 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
E) $1900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

Question 51

Choose the one alternative that best completes the statement or answers the question.
A lab assistant drops a 400.0-g piece of metal at $100.0 ^ { \circ } \mathrm { C }$ into a 100.0-g aluminum cup containing 500.0 g of water at $15.0 ^ { \circ } \mathrm { C }$ In a few minutes, she measures the final temperature of the system to be $40.0 ^ { \circ } \mathrm { C }$ What is the specific heat of the 400.0-g piece of metal, assuming that no significant heat is exchanged with the surroundings? The specific heat of this aluminum is $900.0 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A) $3300 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
B) $3800 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
C) $2270 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
D) $4280 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
E) $1900 \mathrm {~J} / \mathrm { kq } \cdot \mathrm { K }$

Question 52

Choose the one alternative that best completes the statement or answers the question.
A 360-g metal container, insulated on the outside, holds 180.0 g of water in thermal equilibrium at $22.0 ^ { \circ } \mathrm { C }$ A 24.0-g ice cube, at the melting point, is dropped into the water, and when thermal equilibrium is reached the temperature is $15.0 ^ { \circ } \mathrm { C }$ Assume there is no heat exchange with the surroundings. For water, the specific heat capacity is $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the heat of fusion is $3.34 \times$ $10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ What is the specific heat capacity of the metal of the container?

A) 3300 $\mathrm { J } / \mathrm { kq } \cdot \mathrm { K }$
B) 1700 $\mathrm { J } / \mathrm { kq } \cdot \mathrm { K }$
C) 970 $\mathrm { J } / \mathrm { Kg } \cdot \mathrm { K }$
D) 2300 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$
E) 2800 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$

Question 53

Choose the one alternative that best completes the statement or answers the question.
A 44.0-g block of ice at $- 15.0 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter (of neglible heat capacity)
containing 100 g of water at $5.0 ^ { \circ } \mathrm { C }$ When equilibrium is reached, how much of the ice will have
melted? The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

A) 2.1 g
B) 52 g
C) 21 g
D) 4.4 g
E) 5.2 g

Question 54

Choose the one alternative that best completes the statement or answers the question.
A jogger is running outdoors on a cold day when the temperature is $- 20.0 ^ { \circ } \mathrm { C }$ she is breathing at the rate of 25 breaths per minute, and each time she breathes in she inhales $0.00450 \mathrm {~m} ^ { 3 }$ of air. How much heat does she lose from breathing during 20.0 minutes of jogging if the air in her lungs is heated to her body temperature of $37.0 ^ { \circ } \mathrm { C }$ before it is exhaled? The specific heat of air is $1020 \mathrm {~J} / \mathrm { kg }$ K and the density of air under typical conditions is $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 278 kJ
B) 354 kJ
C) 169 kJ
D) 543 kJ
E) 431 kJ

Question 55

Choose the one alternative that best completes the statement or answers the question.
A camper is about to drink his morning coffee. He pours 400 grams of coffee, initially at $75 ^ { \circ } \mathrm { C }$ into a 250-g aluminum cup, initially at $16 ^ { \circ } \mathrm { C }$ What is the equilibrium temperature of the coffee-cup system, assuming no heat is lost to the surroundings? The specific heat of aluminum is 900 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ and the specific heat of coffee is essentially the same as that of water, which is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A) $62 ^ { \circ } \mathrm { C }$
B) $65 ^ { \circ } \mathrm { C }$
C) $68 ^ { \circ } \mathrm { C }$
D) $45 ^ { \circ } \mathrm { C }$
E) $71 ^ { \circ } \mathrm { C }$

Question 56

Choose the one alternative that best completes the statement or answers the question.
A 400-g block of iron at $400 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter (of negligible heat capacity) containing 60 g of water at $30 ^ { \circ } \mathrm { C }$ How much steam is produced? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 }$ J/kg and its specific heat capacity is 4186 $\mathrm { J } / \mathrm { Kg } \cdot \mathrm { K }$ The average specific heat of iron over this temperature range is $560 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$

A) 33 g
B) 22 g
C) 42 g
D) 59 g
E) 54 g

Question 57

Choose the one alternative that best completes the statement or answers the question.
When 50 g of a certain material at $100 ^ { \circ } \mathrm { C }$ is mixed with 100 g of water at $0 ^ { \circ } \mathrm { C }$ the final temperature is $40 ^ { \circ } \mathrm { C }$ What is the specific heat of the material? The specific heat of water is $1.00 \mathrm { kcal } / \mathrm { kq } \cdot \mathrm { C } ^ { \circ }$

A) $0.33 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$
B) $7.5 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$
C) $1.3 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$
D) $0.75 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$

Question 58

Choose the one alternative that best completes the statement or answers the question.
A person makes iced tea by adding ice to 1.8 kg of hot tea, initially at $80 ^ { \circ } \mathrm { C }$ How many kilograms of ice, initially at $0 ^ { \circ } \mathrm { C }$ are required to bring the mixture to $10 ^ { \circ } \mathrm { C } ?$ The specific heat of water (and tea) is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the latent heat of fusion of ice is $3.34 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$

A) 1.2 kg
B) 1.7 kg
C) 1.4 kg
D) 1.0 kg

Question 59

Write the word or phrase that best completes each statement or answers the question.
A piece of iron of mass 0.12 kg is taken from an oven where its temperature is $336 ^ { \circ } \mathrm { C }$ and quickly placed in an insulated copper can that contains 0.20 kg of water. The copper can has mass 0.50 kg, and it and the water in it are originally at a temperature of $20 ^ { \circ } \mathrm { C }$ Calculate the final temperature of the system, assuming no heat is lost to the surroundings. Use the following specific heats: $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \text { (water), } 470 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \text { (iron), }$ and $390 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \text { (copper). }$

Question 60

Write the word or phrase that best completes each statement or answers the question.
How many grams of ice at $- 17 ^ { \circ } \mathrm { C }$ must be added to 741 grams of water that is initially at a temperature of $70 ^ { \circ } \mathrm { C }$ to produce water at a final temperature of $12 ^ { \circ } \mathrm { C } \text { ? }$ Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ and of ice is $2000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ For water the normal melting
point is $0 ^ { \circ } \mathrm { C }$ and the heat of fusion is $334 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { kg }$ The normal boiling point is $100 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $2.256 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg }$

Question 61

Write the word or phrase that best completes each statement or answers the question.
A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water at $100 ^ { \circ } \mathrm { C }$ and the other end in a water-ice mixture at $0 ^ { \circ } \mathrm { C }$ The rod has uniform cross-sectional area $7.05 \mathrm {~cm} ^ { 2 }$ and length 87 cm. The heat conducted by the rod melts the ice at a rate of 1.0 g every 11 seconds. What is the thermal conductivity of the rod? Recall that the heat of fusion of water is $3.34 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$

Question 62

Choose the one alternative that best completes the statement or answers the question.
A heat conducting rod, 1.60 m Iong and wrapped in insulation, is made of an aluminum section
that is 0.90 m long and a copper section that is 0.70 m long. Both sections have a cross-sectional
area of $0.00040 \mathrm {~m} ^ { 2 }$ The aluminum end and the copper end are maintained at temperatures of $30 ^ { \circ } \mathrm { C } \text { and } 170 ^ { \circ } \mathrm { C }$
Respectively. The thermal conductivities of aluminum and copper are 205 W/m . K (aluminum) and $385 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K } \text { (copper). }$ At what rate is heat conducted in the rod under state conditions?

A) 12 W
B) 7.9 W
C) 10 W
D) 11 W
E) 9.0 W

Question 63

Choose the one alternative that best completes the statement or answers the question.
A solid concrete wall has dimensions 4.0 m x 2.4 m and is 30 cm thick. The thermal conductivity of the concrete is $1.3 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ and it separates a basement from the ground outside. The inner surface of the wall is at $18 ^ { \circ } \mathrm { C }$ and the outside surface is at $6 ^ { \circ } \mathrm { C }$ How much heat flows through the wall every hour?

A) 5.0 kJ
B) 500 J
C) 5.0 MJ
D) 1.8 kJ
E) 1.8 MJ

Question 64

Choose the one alternative that best completes the statement or answers the question.
The thermal conductivity of aluminum is twice that of brass. Two rods (one aluminum and the other brass) of the same length and cross-sectional area are joined together end to end. The free end of the brass rod is maintained at $0 ^ { \circ } \mathrm { C }$ and the free end of the aluminum rod is maintained at $200 ^ { \circ } \mathrm { C }$ If no heat escapes from the sides of the rods, what is the temperature at the place where the two rods are joined together?

A) $155 ^ { \circ } \mathrm { C }$
B) $133 ^ { \circ } \mathrm { C }$
C) $148 ^ { \circ } \mathrm { C }$
D) $76 ^ { \circ } \mathrm { C }$

Question 65

Choose the one alternative that best completes the statement or answers the question.
The cylindrical filament in a light bulb has a diameter of 0.050 mm, an emissivity of 1.0 , and a temperature of $3000 ^ { \circ } \mathrm { C } \text {. }$ How long should the filament be in order to radiate 60 W of power? $( \sigma =$ $\left. 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

A) 5.9 cm
B) 7.2 cm
C) 11 cm
D) 8.6 cm
E) 9.4 cm

Question 66

Choose the one alternative that best completes the statement or answers the question.
In an experiment to measure the thermal conductivity of a certain material, a slab of material 10.0 mm thick separates a steam chamber from a block of ice with a square cross-section with dimensions $8.00 \mathrm {~cm} \times 8.00 \mathrm {~cm}$
After 5.00 min of running the experiment, 64.0 g of ice have melted. What is the thermal conductivity of this material? The latent heat of fusion of water is $33.5 \times 10 ^ { 4 }$ J/Kg, the latent heat of vaporization of water is $2.256 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg }$ and both the ice and water are under 1.00 atm of pressure.

A) $0.250 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
B) $0.130 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
C) $0.440 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
D) $1.12 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
E) $0.620 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$

Question 67

Choose the one alternative that best completes the statement or answers the question.
Two metal rods, one silver and the other gold, are attached to each other end-to-end. The free end of the silver rod is immersed in a steam chamber at $100 ^ { \circ } \mathrm { C } ,$ and the free end of the gold rod in an ice water bath at $0 ^ { \circ } \mathrm { C }$ The rods are both 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the ends. How much total heat flows through the two rods each minute? The thermal conductivity of silver is 417 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ and that of gold is 291 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$

A) 8.2 kJ
B) 12 kJ
C) 14 kJ
D) 9.5 kJ
E) 16 kJ

Question 68

Choose the one alternative that best completes the statement or answers the question.
The thermal conductivity of a certain concrete is 0.80 $\mathrm { W } / \mathrm { m } , \mathrm { K }$ and the thermal conductivity of a certain wood is 0.10 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ How thick would a solid concrete wall have to be in order to have the same rate of heat flow through it as an 8.0-cm thick wall made of solid wood? Both walls have the same surface area and the same temperature difference across their faces.

A) 53 cm
B) 64 cm
C) 85 cm
D) 71 cm

Question 69

Choose the one alternative that best completes the statement or answers the question.
Two metal rods, one silver and the other copper, are both immersed at one end in a steam chamber at a temperature of $100 ^ { \circ } \mathrm { C } \text {. }$ The other end of each one is in an ice water bath at $0 ^ { \circ } \mathrm { C }$ The rods are 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and the surroundings, except at the ends. How much total heat flows through the two rods each minute? The thermal conductivity of silver is $417 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ and that of copper is 395 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } .$

A) 47 kJ
B) 49 kJ
C) 39 kJ
D) 20 kJ
E) 11 kJ

Question 70

Choose the one alternative that best completes the statement or answers the question.
A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have cross-sectional areas of 0.0020 $m ^ { 2 }$ The thermal conductivity of alloy B is known to be 1.8 times as great as that for alloy A . The end of the rod in alloy A is maintained at a temperature of $10 ^ { \circ } \mathrm { C }$ and the other end of the rod is maintained at an unknown temperature. When steady state flow has been established, the temperature at the junction of the alloys is measured to be $40 ^ { \circ } \mathrm { C }$ and the rate of heat flow in the rod is measured at 56 W. What is the thermal conductivity of alloy A?

A) $130 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
B) $140 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
C) $120 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
D) $135 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
E) $125 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$

Question 71

Choose the one alternative that best completes the statement or answers the question.
A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow through the wall by 90 percent. The inner surface of the wooden wall is maintained at $- 10 ^ { \circ } \mathrm { C }$ and the outer surface of the concrete wall is at $20 ^ { \circ } \mathrm { C }$ The thermal conductivities of concrete and wood are 0.80 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ (concrete) and 0.040 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ (wood). What should be the thickness of the layer of wood?

A) 60 mm
B) 100 mm
C) 90 mm
D) 70 mm
E) 80 mm

Question 72

Choose the one alternative that best completes the statement or answers the question.
A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B , joined end-to-end. Both pieces have cross-sectional areas of 0.0020 $\mathrm { m } ^ { 2 }$ The thermal conductivity of alloy B is known to be 1.8 times as great as that for alloy A. The end of the rod in alloy A is maintained at a temperature of $10 ^ { \circ } \mathrm { C }$ and the other end of the rod is maintained at an unknown temperature. When steady state flow has been established, the temperature at the junction of the alloys is measured to be $40 ^ { \circ } \mathrm { C } ,$ and the rate of heat flow in the rod is measured at 56 W. What is the temperature of the end of the rod in alloy B?

A) $80 ^ { \circ } \mathrm { C }$
B) $84 ^ { \circ } \mathrm { C }$
C) $96 ^ { \circ } \mathrm { C }$
D) $92 ^ { \circ } \mathrm { C }$
E) $88 ^ { \circ } \mathrm { C }$

Question 73

Choose the one alternative that best completes the statement or answers the question.
A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow through the wall by 90 percent. The inner surface of the wooden wall is maintained at $- 10 ^ { \circ } \mathrm { C }$ and the outer surface of the concrete wall is at $20 ^ { \circ } \mathrm { C }$ The thermal conductivities of concrete and wood are $0.80$ $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ (concrete) and 0.040 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } \text { (wood) }$ What is the temperature difference across the layer of wood?

A) $25 \mathrm { C } ^ { \circ }$
B) $27 \mathrm { C } ^ { \circ }$
C) $24 C ^ { \circ }$
D) $28 \mathrm { C } ^ { \circ }$
E) $26 \mathrm { C } ^ { \circ }$

Question 74

Choose the one alternative that best completes the statement or answers the question.
A heat-conducting rod, 0.90 m long and wrapped in insulation, is made of an aluminum section
that is 0.20 m Iong and a copper section that is 0.70 m long. Both sections have a cross-sectional area of $0.00040 \mathrm {~m} ^ { 2 }$ The aluminum end and the copper end are maintained at temperatures of $30 ^ { \circ } \mathrm { C } \text { and } 230 ^ { \circ } \mathrm { C }$ respectively. The thermal conductivities of aluminum and copper are 205 W/m . K (aluminum) and $385 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K } \text { (copper). }$ What is the temperature of the aluminum-copper
junction in the rod with steady state heat flow?

A) $80 ^ { \circ } \mathrm { C }$
B) $100 ^ { \circ } \mathrm { C }$
C) $74 ^ { \circ } \mathrm { C }$
D) $86 ^ { \circ } \mathrm { C }$
E) $93 ^ { \circ } \mathrm { C }$

Question 75

Choose the one alternative that best completes the statement or answers the question.
Two metal rods, one silver and the other gold, are attached to each other end-to-end. The free end of the silver rod is immersed in a steam chamber at $100 ^ { \circ } \mathrm { C }$ and the free end of the gold rod in an ice water bath at $0 ^ { \circ } \mathrm { C }$ The rods are both 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the ends. What is the temperature at the point where the two rods are in contact with one another? The thermal conductivity of silver is 417 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } .$ and that of gold is 291 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } .$

A) $47 ^ { \circ } \mathrm { C }$
B) $59 ^ { \circ } \mathrm { C }$
C) $53 ^ { \circ } \mathrm { C }$
D) $41 ^ { \circ } \mathrm { C }$
E) $39 ^ { \circ } \mathrm { C }$

Question 76

Choose the one alternative that best completes the statement or answers the question.
Some properties of a certain glass are listed here:
Density $2300 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
Specific heat capacity $\quad 840 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$
Coefficient of thermal expansion $8.5 \times 10 ^ { - 6 } \left( \mathrm { C } ^ { \circ } \right) ^ { - 1 }$
Thermal conductivity $\quad 0.80 \mathrm {~W} / \mathrm { m } \cdot \mathrm { C } ^ { \circ }$
A glass window pane is 2.7 m high, 2.4 m wide, and 9.0 mm thick. The temperature at the inner surface of the glass is $19 ^ { \circ } \mathrm { C }$ and at the outer surface $4 ^ { \circ } \mathrm { C }$ How much heat is lost each hour through the window?

A) $3.1 \times 10 ^ { 7 } \mathrm {~J}$
B) $3.1 \times 10 ^ { 5 } \mathrm {~J}$
C) $8.6 \times 10 ^ { 3 } \mathrm {~J}$
D) $3.1 \times 10 ^ { 4 } \mathrm {~J}$
E) 8.6 J

Question 77

Choose the one alternative that best completes the statement or answers the question.
A 400-g stainless steel tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that is in contact with the heating element has an area of $0.090 \mathrm {~m} ^ { 2 }$ and is 2.0 mm thick. At a certain moment, the temperature of the water is $75 ^ { \circ } \mathrm { C }$ and it is rising at the rate of $3.0 \mathrm { C } ^ { \circ }$ per minute. What is the difference in temperature between the inside and the outside of the bottom of the tea kettle? Assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of stainless steel is $16.3 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ the specific heat of the steel is 448 $\mathrm { J } / \mathrm { Kg } \cdot \mathrm { K }$ and the specific heat of water is 4186 $\text { J/kg. K. }$

A) $0.15 \mathrm { C } ^ { \circ }$
B) $1.1 \mathrm { C } ^ { \circ }$
C) $2.2 \mathrm { C } ^ { \circ }$
D) $0.50 \mathrm { C } ^ { \circ }$
E) $1.5 \mathrm { C } ^ { \circ }$

Question 78

Choose the one alternative that best completes the statement or answers the question.
A glass tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that is in contact with the heating element has an area of $0.090 \mathrm {~m} ^ { 2 }$ and is 1.5 mm thick. At a certain moment, the temperature of the water is $75 ^ { \circ } \mathrm { C }$ and it is rising at the rate of $3 \mathrm { C } ^ { \circ }$ per minute. What is the temperature of the outside surface of the bottom of the tea kettle? Neglect the heat capacity of the kettle, and assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of glass is $0.840 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ and the specific heat of water is 4186 $\mathrm { J } / \mathrm { kq } \cdot \mathrm { K }$

A) $86 ^ { \circ } \mathrm { C }$
B) $77 ^ { \circ } \mathrm { C }$
C) $92 ^ { \circ } \mathrm { C }$
D) $120 ^ { \circ } \mathrm { C }$
E) $39 ^ { \circ } \mathrm { C }$

Question 79

Choose the one alternative that best completes the statement or answers the question.
A window glass that is 0.5 cm thick has dimensions of 3 m by 1.5 m. The thermal conductivity of this glass is 0.8 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ If the outside surface of the glass is at $- 10 ^ { \circ } \mathrm { C }$ and the inside surface is at $20 ^ { \circ } \mathrm { C }$ how much heat flows through the window in every hour?

A) 80 MJ
B) 60 MJ
C) 70 MJ
D) 50 MJ

Question 80

Choose the one alternative that best completes the statement or answers the question.
A sphere of surface area $1.25 \mathrm {~m} ^ { 2 }$ and emissivity 1.0 is at a temperature of $100 ^ { \circ } \mathrm { C }$ At what rate does it radiate heat into empty space? $\left( \sigma = 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

A) 7.1 W
B) 0.71 mW
C) 3.7 W
D) 9.9 mW
E) 1.4 kW