Deck 14: Heat

Question 1

What is the change in internal energy of 2.00 moles of a monatomic ideal gas as it is heated from $0 \mathrm{~K}$ to 100 $\mathrm{K}$ ?

A) $2,490 \mathrm{~J}$
B) $1,950 \mathrm{~J}$
C) $2,750 \mathrm{~J}$
D) $3,250 \mathrm{~J}$
E) $3,670 \mathrm{~J}$

Answer 1

$2,490 \mathrm{~J}$

Question 2

If the temperature of 2.000 moles of a monatomic ideal gas is increased by $50^{\circ} \mathrm{C}$ , then what is the increase in the internal energy of the gas?

A) $1,980 \mathrm{~J}$
B) $3,030 \mathrm{~J}$
C) $2,750 \mathrm{~J}$
D) $1,247 \mathrm{~J}$
E) $2,250 \mathrm{~J}$

Answer 2

$1,247 \mathrm{~J}$

Question 3

What is the change in internal energy of 2.00 moles of a monatomic ideal gas that cools from 200 ${ }^{\circ} \mathrm{C}$ to $-50^{\circ} \mathrm{C}$ ?

A) $-13,049 \mathrm{~J}$
B) $-6,236 \mathrm{~J}$
C) $-750 \mathrm{~J}$
D) $-3,742 \mathrm{~J}$
E) $-500 \mathrm{~J}$

Answer 3

$-6,236 \mathrm{~J}$

Question 4

A person of mass $90.0 \mathrm{~kg}$ walks up a flight of stairs that are 12.0 meters high. What is the required energy of the exercise in Calories?

A) 1.85
B) 8.55
C) 4.66
D) 2.53
E) 7.32

Question 5

A person lifts $10.00 \mathrm{~N}$ weights a vertical distance of $50.00 \mathrm{~cm}$ . How many times would they have to lift the weight to use 10.00 Calories of energy?

A) 7,503
B) 4,125
C) 8,370
D) 9,670
E) 5,170

Question 6

200 joules of heat flows into a $35.0 \mathrm{~g}$ sample. If the temperature increases by $10.0^{\circ} \mathrm{C}$ , then what is the specific heat capacity of the sample, in $\mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C}$ ?

A) 375
B) 571
C) 254
D) 175
E) 422

Question 7

Water has a specific heat capacity of $4,186 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ . A tank contains $500 \mathrm{~kg}$ of water at $10.0{ }^{\circ} \mathrm{C}$ . The water is heated to a temperature of $90.0^{\circ} \mathrm{C}$ . If electricity costs $\$ 0.100$ per kilowatt-hour, then what is the cost of heating the water?

A) $\$ 3.79$
B) $\$ 8.75$
C) $\$ 4.65$
D) $\$ 6.22$
E) $\$ 3.10$

Question 8

A $100 \mathrm{~g}$ glass container is at $10.0^{\circ} \mathrm{C} .200 \mathrm{~g}$ of water at $90.0^{\circ} \mathrm{C}$ is added to the glass container. What is the final temperature of the water and the glass, in ${ }^{\circ} \mathrm{C}$ ? (specific heat of water $=1.00 \mathrm{cal} / \mathrm{g}{ }^{\circ} \mathrm{C}$ , specific heat of glass $=0.200 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$ )

A) 50.2
B) 46.9
C) 68.2
D) 82.7
E) 75.0

Question 9

A $100 \mathrm{~g}$ glass container contains $250 \mathrm{~g}$ of water at $15.0^{\circ} \mathrm{C}$ . A $20.0 \mathrm{~g}$ piece of lead at $100{ }^{\circ} \mathrm{C}$ is added to the water in the container. What is the final temperature of the system in ${ }^{\circ} \mathrm{C}$ ? (specific heat of water $=1.00 \mathrm{cal} / \mathrm{g}$ ${ }^{\circ} \mathrm{C}$ , specific heat of glass $=0.200 \mathrm{cal} / \mathrm{g}{ }^{\circ} \mathrm{C}$ , specific heat of lead $=0.0310 \mathrm{cal} / \mathrm{g}{ }^{\circ} \mathrm{C}$ )

A) 25.0
B) 15.2
C) 10.1
D) 31.4
E) 46.3

Question 10

A $100 \mathrm{~g}$ glass container contains $250 \mathrm{~g}$ of water at $15.0^{\circ} \mathrm{C}$ . A $100 \mathrm{~g}$ piece of unknown material at $100{ }^{\circ} \mathrm{C}$ is added to the water in the container. The final temperature of the mixture is $19.0^{\circ} \mathrm{C}$ . What is the specific heat of the unknown material in $\mathrm{J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ ? (specific heat of water $=4,186 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , specific heat of glass $=837.2$ $\mathrm{J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ )

A) 558
B) 674
C) 245
D) 412
E) 387

Question 11

A 50.0 g glass container contains $200 \mathrm{~g}$ of water at $20.0^{\circ} \mathrm{C}$ . A $20.0 \mathrm{~g}$ piece of an alloy at $100{ }^{\circ} \mathrm{C}$ is added to the water in the container. The final temperature of the mixture is $24^{\circ} \mathrm{C}$ . What is the specific heat of the alloy in cal/g ${ }^{\circ} \mathrm{C}$ ? (specific heat of water $=1.00 \mathrm{cal} / \mathrm{g}{ }^{\circ} \mathrm{C}$ , specific heat of glass $=0.200 \mathrm{cal} / \mathrm{g}{ }^{\circ} \mathrm{C}$ )

A) 0.553
B) 1.54
C) 2.75
D) 0.852
E) 1.87

Question 12

What is the heat needed to heat $150 \mathrm{~g}$ of water from $10.0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ ? (specific heat of water $=4,186$ $\mathrm{J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ )

A) $44.6 \mathrm{~kJ}$
B) $37.2 \mathrm{~kJ}$
C) $56.5 \mathrm{~kJ}$
D) $68.2 \mathrm{~kJ}$
E) $75.1 \mathrm{~kJ}$

Question 13

The molar specific heat of a diatomic ideal gas at constant volume is $\mathrm{Cv}=5 / 2 \mathrm{R}$ . What is the heat needed to heat $28.00 \mathrm{~g}$ of nitrogen gas from $20.00^{\circ} \mathrm{C}$ to $85.00^{\circ} \mathrm{C}$ ?

A) $1,753 \mathrm{~J}$
B) $2,890 \mathrm{~J}$
C) $1,350 \mathrm{~J}$
D) $1,443 \mathrm{~J}$
E) $1,540 \mathrm{~J}$

Question 14

What is the heat needed to heat 16.0 grams of helium gas at constant volume from $20.0^{\circ} \mathrm{C}$ to $85.0{ }^{\circ} \mathrm{C}$ ?

A) $0.650 \mathrm{~kJ}$
B) $3.24 \mathrm{~kJ}$
C) $1.95 \mathrm{~kJ}$
D) $2.02 \mathrm{~kJ}$
E) $4.23 \mathrm{~kJ}$

Question 15

A sample of helium has a volume of 2.00 liters, a temperature of $20.0^{\circ} \mathrm{C}$ , and a pressure of 2.50 atmospheres. What is the energy needed to heat the sample of helium gas from $20.0^{\circ} \mathrm{C}$ to $95.0^{\circ} \mathrm{C}$ at constant volume?

A) $476 \mathrm{~J}$
B) $88.0 \mathrm{~J}$
C) $137 \mathrm{~J}$
D) $207 \mathrm{~J}$
E) $194 \mathrm{~J}$

Question 16

The heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ . What is the energy needed to melt 100 grams of ice at 0.00 ${ }^{\circ} \mathrm{C}$ ?

A) $39.4 \mathrm{~kJ}$
B) $12.7 \mathrm{~kJ}$
C) $33.4 \mathrm{~kJ}$
D) $25.5 \mathrm{~kJ}$
E) $17.5 \mathrm{~kJ}$

Question 17

The heat of fusion for lead at $327.0{ }^{\circ} \mathrm{C}$ is $22.9 \mathrm{~kJ} / \mathrm{kg}$ and the specific heat of lead is $0.130 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ . What is the energy needed to melt 100 grams of lead starting at $0{ }^{\circ} \mathrm{C}$ ?

A) $3.56 \mathrm{~kJ}$
B) $7.76 \mathrm{~kJ}$
C) $4.23 \mathrm{~kJ}$
D) $7.02 \mathrm{~kJ}$
E) $6.54 \mathrm{~kJ}$

Question 18

The heat of fusion for gold at $1,063{ }^{\circ} \mathrm{C}$ is $66.6 \mathrm{~kJ} / \mathrm{kg}$ and the specific heat of gold is $0.128 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ . What is the energy needed to melt 100 grams of gold starting at $0{ }^{\circ} \mathrm{C}$ ?

A) $17.8 \mathrm{~kJ}$
B) $9.50 \mathrm{~kJ}$
C) $7.50 \mathrm{~kJ}$
D) $12.3 \mathrm{~kJ}$
E) $20.3 \mathrm{~kJ}$

Question 19

The heat of fusion for silver at $960.8{ }^{\circ} \mathrm{C}$ is $88.3 \mathrm{~kJ} / \mathrm{kg}$ and the specific heat of silver is $0.235 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ . What is the energy needed to melt 100 grams of silver starting at $0{ }^{\circ} \mathrm{C}$ ?

A) $31.4 \mathrm{~kJ}$
B) $13.7 \mathrm{~kJ}$
C) $25.4 \mathrm{~kJ}$
D) $40.5 \mathrm{~kJ}$
E) $19.5 \mathrm{~kJ}$

Question 20

The heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of water at $100{ }^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ . What is the energy needed to vaporize 100 grams of ice at starting at $0{ }^{\circ} \mathrm{C}$ ?

A) $259.0 \mathrm{~kJ}$
B) $33.37 \mathrm{~kJ}$
C) $41.86 \mathrm{~kJ}$
D) $225.6 \mathrm{~kJ}$
E) $300.8 \mathrm{~kJ}$

Question 21

The heat of fusion for lead at $327^{\circ} \mathrm{C}$ is $22.9 \mathrm{~kJ} / \mathrm{kg}$ and the specific heat of solid lead is $0.130 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the specific heat of liquid lead is $0.0900 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of lead at $1,620^{\circ} \mathrm{C}$ is $871 \mathrm{~kJ} / \mathrm{kg}$ . What is the energy needed to vaporize 100 grams of lead starting at $0^{\circ} \mathrm{C}$ ?

A) $156 \mathrm{~kJ}$
B) $189 \mathrm{~kJ}$
C) $105 \mathrm{~kJ}$
D) $147 \mathrm{~kJ}$
E) $176 \mathrm{~kJ}$

Question 22

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of water at $100^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ . What is the final equilibrium temperature when 10.0 grams of ice at $-15^{\circ} \mathrm{C}$ is mixed with 40.0 grams of water at $75^{\circ} \mathrm{C}$ ?

A) $53.6^{\circ} \mathrm{C}$
B) $48.9^{\circ} \mathrm{C}$
C) $59.5^{\circ} \mathrm{C}$
D) $42.6^{\circ} \mathrm{C}$
E) $57.2^{\circ} \mathrm{C}$

Question 23

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of water at $100^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ . What is the final equilibrium temperature when 5.00 grams of ice at $-15.0^{\circ} \mathrm{C}$ is mixed with 40.0 grams of water at $75.0^{\circ} \mathrm{C}$ ?

A) $57.0^{\circ} \mathrm{C}$
B) $16.1^{\circ} \mathrm{C}$
C) $20.9^{\circ} \mathrm{C}$
D) $28.3^{\circ} \mathrm{C}$
E) $18.6^{\circ} \mathrm{C}$

Question 24

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of water at $100^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ . What is the final equilibrium temperature when 10.0 grams of ice at $-15.0^{\circ} \mathrm{C}$ is mixed with 3.00 grams of steam at $100^{\circ} \mathrm{C}$ ?

A) $60.2^{\circ} \mathrm{C}$
B) $76.4^{\circ} \mathrm{C}$
C) $70.2^{\circ} \mathrm{C}$
D) $65.0^{\circ} \mathrm{C}$
E) $80.3^{\circ} \mathrm{C}$

Question 25

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of water at $100^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ . What is the final equilibrium temperature when 20.0 grams of ice at $-15.0^{\circ} \mathrm{C}$ is mixed with 5.00 grams of steam at $100^{\circ} \mathrm{C}$ ?

A) $52.7^{\circ} \mathrm{C}$
B) $44.1^{\circ} \mathrm{C}$
C) $48.9^{\circ} \mathrm{C}$
D) $58.0^{\circ} \mathrm{C}$
E) $65.2^{\circ} \mathrm{C}$

Question 26

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of water at $100^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ . What is the final equilibrium temperature when 30.0 grams of ice at $-15.0^{\circ} \mathrm{C}$ is mixed with 8.00 grams of steam at $100^{\circ} \mathrm{C}$ ?

A) $56.2^{\circ} \mathrm{C}$
B) $50.1^{\circ} \mathrm{C}$
C) $45.2^{\circ} \mathrm{C}$
D) $65.6^{\circ} \mathrm{C}$
E) $60.2^{\circ} \mathrm{C}$

Question 27

The heat of vaporization of water at $100.0^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ . What is the heat of vaporization of water in $\mathrm{cal} / \mathrm{g}$ ?

A) 497.2
B) 418.6
C) 365.3
D) 684.1
E) 538.9

Question 28

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of vaporization of water at $100^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ , and the specific heat of steam is $2.020 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ . What is the final equilibrium temperature when 40.0 grams of ice at $0{ }^{\circ} \mathrm{C}$ is mixed with 5.00 grams of steam at $120^{\circ} \mathrm{C}$ ?

A) $1.07^{\circ} \mathrm{C}$
B) $1.21^{\circ} \mathrm{C}$
C) $3.01{ }^{\circ} \mathrm{C}$
D) $0.90^{\circ} \mathrm{C}$
E) $2.65^{\circ} \mathrm{C}$

Question 29

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of vaporization of water at $100^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ , and the specific heat of steam is $2.020 \mathrm{~kJ} / \mathrm{kg}^{\circ} \mathrm{C}$ . What is the final equilibrium temperature when 30.0 grams of ice at $0{ }^{\circ} \mathrm{C}$ is mixed with 4.00 grams of steam at $120^{\circ} \mathrm{C}$ ?

A) $3.02^{\circ} \mathrm{C}$
B) $8.77^{\circ} \mathrm{C}$
C) $18.4^{\circ} \mathrm{C}$
D) $5.97^{\circ} \mathrm{C}$
E) $10.2^{\circ} \mathrm{C}$

Question 30

The specific heat of steam is $2,020 \mathrm{~J} / \mathrm{kg} \mathrm{K}$ in SI units. What is the value of the specific heat of steam in cal/g ${ }^{\circ} \mathrm{C}$ ?

A) 0.6812
B) 0.8765
C) 1.000
D) 0.2563
E) 0.4826

Question 31

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of vaporization of water at $100^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ , and the specific heat of steam is $2.020 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ . What is the final equilibrium temperature when 40.0 grams of ice at $0{ }^{\circ} \mathrm{C}$ is mixed with 8.00 grams of steam at $120^{\circ} \mathrm{C}$ ?

A) $38.76^{\circ} \mathrm{C}$
B) $50.22^{\circ} \mathrm{C}$
C) $41.67^{\circ} \mathrm{C}$
D) $25.67^{\circ} \mathrm{C}$
E) $32.55^{\circ} \mathrm{C}$

Question 32

The specific heat of water is $1.000 \mathrm{cal} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)$ . What is the specific heat of water in SI units?

A) $2,765 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$
B) $2,124 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$
C) $3,417 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$
D) $4,186 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$
E) $3,764 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$

Question 33

The specific heat of ice is $2.100 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of water at $100{ }^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{k}$ . What is the final equilibrium temperature when 10.00 grams of ice at $-15.00^{\circ} \mathrm{C}$ is mixed with 2.00 grams of steam at $100.0^{\circ} \mathrm{C}$ ?

A) $40.12^{\circ} \mathrm{C}$
B) $45.711^{\circ} \mathrm{C}$
C) $53.53^{\circ} \mathrm{C}$
D) $33.79^{\circ} \mathrm{C}$
E) $27.54^{\circ} \mathrm{C}$

Question 34

The specific heat of ice is $2.100 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , and the heat of vaporization of water at $100.0^{\circ} \mathrm{C}$ is 2,256 $\mathrm{kJ} / \mathrm{kg}$ . What is the final equilibrium temperature when 10.00 grams of ice at $-15^{\circ} \mathrm{C}$ is mixed with 3.000 grams of steam at $100{ }^{\circ} \mathrm{C}$ ?

A) $78.45^{\circ} \mathrm{C}$
B) $80.34^{\circ} \mathrm{C}$
C) $85.32^{\circ} \mathrm{C}$
D) $82.56^{\circ} \mathrm{C}$
E) $87.21^{\circ} \mathrm{C}$

Question 35

The specific heat of ice is $2.10 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}^{\circ} \mathrm{C}$ , the heat of vaporization of water at $100{ }^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ , and the specific heat of steam is $2.020 \mathrm{~kJ} / \mathrm{kg}^{\circ} \mathrm{C}$ . What is the final equilibrium temperature when 10.0 grams of ice at $-15.0^{\circ} \mathrm{C}$ is mixed with 2.00 grams of steam at $120^{\circ} \mathrm{C}$ ?

A) $39.5^{\circ} \mathrm{C}$
B) $40.1^{\circ} \mathrm{C}$
C) $35.4^{\circ} \mathrm{C}$
D) $37.2^{\circ} \mathrm{C}$
E) $33.2^{\circ} \mathrm{C}$

Question 36

The specific heat of ice is $2.100 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of fusion for ice at $0{ }^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$ , the specific heat of water $4.186 \mathrm{~kJ} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , the heat of vaporization of water at $100.0^{\circ} \mathrm{C}$ is $2,256 \mathrm{~kJ} / \mathrm{kg}$ , and the specific heat of steam is $2.020 \mathrm{~kJ} / \mathrm{kg}^{\circ} \mathrm{C}$ . What is the final equilibrium temperature when 20.00 grams of ice at $-15.0^{\circ} \mathrm{C}$ is mixed with 5.000 grams of steam at $120.0^{\circ} \mathrm{C}$ ?

A) $56.03^{\circ} \mathrm{C}$
B) $59.92^{\circ} \mathrm{C}$
C) $45.67^{\circ} \mathrm{C}$
D) $49.34^{\circ} \mathrm{C}$
E) $52.76^{\circ} \mathrm{C}$

Question 37

A 100 gram glass container contains 200 grams of water and 5 grams of ice all at $0{ }^{\circ} \mathrm{C}$ . A 200 gram piece of lead at $100^{\circ} \mathrm{C}$ is added to the water and ice in the container. What is the final temperature of the system? (specific heat of ice $=2,000 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , specific heat of water $=4,186 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , heat of fusion of water $=333.7$ $\mathrm{kJ} / \mathrm{kg}$ , specific heat of glass $=837.2 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , specific heat of lead $=127.7 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ )

A) $4.87^{\circ} \mathrm{C}$
B) $2.19^{\circ} \mathrm{C}$
C) $3.65^{\circ} \mathrm{C}$
D) $0.915^{\circ} \mathrm{C}$
E) $5.33{ }^{\circ} \mathrm{C}$

Question 38

A 100 gram glass container contains 200 grams of water and 10 grams of ice all at $0{ }^{\circ} \mathrm{C}$ . A 200 gram piece of lead at $100^{\circ} \mathrm{C}$ is added to the water and ice in the container. What is the final temperature of the system? (specific heat of ice $=2,000 \mathrm{~J} / \mathrm{kg}^{\circ} \mathrm{C}$ , specific heat of water $=4,186 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , heat of fusion of water $=333.7$ $\mathrm{kJ} / \mathrm{kg}$ , specific heat of glass $=837.2 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ , specific heat of lead $=127.7 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ )

A) $2.86{ }^{\circ} \mathrm{C}$
B) $0{ }^{\circ} \mathrm{C}$
C) $4.01^{\circ} \mathrm{C}$
D) $1.85^{\circ} \mathrm{C}$
E) $3.43^{\circ} \mathrm{C}$

Question 39

A metal rod is placed between two temperature sources so that heat can flow between them. One temperature is $90.0^{\circ} \mathrm{C}$ and the other temperature is $25.0^{\circ} \mathrm{C}$ . The length of the rod is $30.0 \mathrm{~cm}$ and the cross-sectional area is $10.0 \mathrm{~cm}^{2}$ . If 15.0 watts of heat flows between the hot temperature and the cold temperature, then what is the thermal conductivity for the metal?

A) $69.2 \mathrm{~W} /\left(\mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)$
B) $46.3 \mathrm{~W} /\left(\mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)$
C) $50.4 \mathrm{~W} /\left(\mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)$
D) $58.2 \mathrm{~W} /\left(\mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)$
E) $44.2 \mathrm{~W} /\left(\mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)$

Question 40

A brass rod with a length of $10.0 \mathrm{~cm}$ is placed end to end with an aluminum rod with a length of $30.0 \mathrm{~cm}$ , and this system is placed between a hot temperature of $100^{\circ} \mathrm{C}$ and a cold temperature of $10.0^{\circ} \mathrm{C}$ . The thermal conductivities of the brass and the aluminum are $100 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$ and $230 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$ , respectively. The rods have the same cross-sectional area of $20.0 \mathrm{~cm}^{2}$ . What is the heat flow from the hot temperature to the cold temperature?

A) $55.3 \mathrm{~W}$
B) $65.3 \mathrm{~W}$
C) $78.1 \mathrm{~W}$
D) $70.3 \mathrm{~W}$
E) $85.3 \mathrm{~W}$

Question 41

A brass rod with a length of $20.0 \mathrm{~cm}$ is placed end to end with an aluminum rod with a length of $20.0 \mathrm{~cm}$ , and this system is placed between a hot temperature of $100^{\circ} \mathrm{C}$ and a cold temperature of $10.0^{\circ} \mathrm{C}$ . The thermal conductivities of the brass and the aluminum are $100 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$ and $230 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C}$ , respectively. The rods have the same cross-sectional area of $25.0 \mathrm{~cm}^{2}$ . What is the heat flow from the hot temperature to the cold temperature?

A) $70.2 \mathrm{~W}$
B) $55.5 \mathrm{~W}$
C) $78.4 \mathrm{~W}$
D) $65.3 \mathrm{~W}$
E) $61.5 \mathrm{~W}$

Question 42

A Styrofoam cooler has a surface area of $2,700 \mathrm{~cm}^{2}$ and a wall thickness of $3.0 \mathrm{~cm}$ . Styrofoam has a thermal conductivity of $0.010 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$ . A $2.0 \mathrm{~kg}$ block of ice is placed inside the cooler that has a temperature inside of $2.0^{\circ} \mathrm{C}$ . If the heat of fusion for ice is $333.7 \mathrm{~kJ} / \mathrm{kg}$ and the temperature outside is $35.0^{\circ} \mathrm{C}$ , then how long will the ice last? Ignore the effect of the air inside the cooler.

A) 42 hours
B) 55 hours
C) 74 hours
D) 24 hours
E) 62 hours

Question 43

A brass rod with a length of $30.0 \mathrm{~cm}$ is placed side by side with an aluminum rod with a length of $30.0 \mathrm{~cm}$ , and this system is placed between a hot temperature of $100^{\circ} \mathrm{C}$ and a cold temperature of $10.0^{\circ} \mathrm{C}$ . The thermal conductivities of the brass and the aluminum are $100 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$ and $230 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C}$ , respectively. The brass rod has a cross-sectional area of $20.0 \mathrm{~cm}^{2}$ , and the aluminum rod has a cross-sectional area of 30.0 $\mathrm{cm}^{2}$ . What is the rate of heat flow from the hot temperature to the cold temperature?

A) $267 \mathrm{~W}$
B) $542 \mathrm{~W}$
C) $54.2 \mathrm{~W}$
D) $26.7 \mathrm{~W}$

Question 44

A Styrofoam cooler has a surface area of $2,700 \mathrm{~cm}^{2}$ and a wall thickness of $3.00 \mathrm{~cm}$ . Styrofoam has a thermal conductivity of $0.010 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C}$ . A $2.00 \mathrm{~kg}$ block of ice is placed inside the cooler that has a temperature inside of $2^{\circ} \mathrm{C}$ . When the temperature outside is $30.0^{\circ} \mathrm{C}$ , the ice lasts for 8.00 hours. If the temperature outside becomes $20.0^{\circ} \mathrm{C}$ , then how long will the ice last? Ignore the effect of the air inside the cooler.

A) $12.4 \mathrm{hr}$
B) $18.5 \mathrm{hr}$
C) $20.3 \mathrm{hr}$
D) $10.1 \mathrm{hr}$
E) $8.5 \mathrm{hr}$

Question 45

A concrete wall is $15.0 \mathrm{~cm}$ thick and has an area of $10.0 \mathrm{~m}^{2}$ . A layer of wood that is $2.50 \mathrm{~cm}$ thick is placed over the wall to reduce the loss of heat by thermal conduction. The thermal conductivity of concrete is 1.70 $\mathrm{W} / \mathrm{m}^{\circ} \mathrm{C}$ and the thermal conductivity of wood is $0.0400 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$ . What is the effective thermal conductivity of the wood-on-concrete system?

A) $1.65 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C}$
B) $2.34 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$
C) $1.22 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$
D) $2.02 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$
E) $0.245 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$

Question 46

A brass rod with a length of $20.0 \mathrm{~cm}$ is placed side by side with an aluminum rod with a length of $20.0 \mathrm{~cm}$ , and this system is placed between a hot temperature of $150^{\circ} \mathrm{C}$ and a cold temperature of $-10.0^{\circ} \mathrm{C}$ . The thermal conductivities of the brass and the aluminum are $100 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C}$ and 230 $\mathrm{W} / \mathrm{m}^{\circ} \mathrm{C}$ , respectively. The rods have the same cross-sectional area of $20.0 \mathrm{~cm}^{2}$ . What is the rate of heat flow from the hot temperature to the cold temperature?

A) $683 \mathrm{~W}$
B) $52.8 \mathrm{~W}$
C) $528 \mathrm{~W}$
D) $68.3 \mathrm{~W}$

Question 47

A jogger runs a kilometer in 8.30 minutes in still, dry air at a temperature of $25.0^{\circ} \mathrm{C}$ . Her skin has a temperature of $35.0{ }^{\circ} \mathrm{C}$ and an exposed area of $1.00 \mathrm{~m}^{2}$ . If the convective coefficient is $22.0 \mathrm{~W} / \mathrm{m}^{2}{ }^{\circ} \mathrm{C}$ , then what is the rate of heat flow due to convection from her skin to the air?

A) $186 \mathrm{~W}$
B) $220 \mathrm{~W}$
C) $285 \mathrm{~W}$
D) $102 \mathrm{~W}$
E) $95.7 \mathrm{~W}$

Question 48

The intensity of solar radiation reaching the Earth is $1,340 \mathrm{~W} / \mathrm{m}^{2}$ . If the sun has a radius of $7.000 \times 10^{8} \mathrm{~m}$ , is a perfect radiator and is located $1.500 \times 10^{11} \mathrm{~m}$ from the Earth, then what is the temperature of the sun?

A) $3,210 \mathrm{~K}$
B) $5,740 \mathrm{~K}$
C) $3,670 \mathrm{~K}$
D) $6,430 \mathrm{~K}$
E) $4,230 \mathrm{~K}$

Question 49

The outer surface of a wood-burning stove in a cabin is at a temperature of $150^{\circ} \mathrm{C}$ . What is the wavelength at which the blackbody radiation is a maximum?

A) $4.02 \mu \mathrm{m}$
B) $6.85 \mu \mathrm{m}$
C) $4.57 \mu \mathrm{m}$
D) $5.25 \mu \mathrm{m}$
E) $3.64 \mu \mathrm{m}$

Question 50

The intensity of solar radiation reaching the Earth is $1,340 \mathrm{~W} / \mathrm{m}^{2}$ when the temperature of the Sun is $5,800 \mathrm{~K}$ . If the temperature of the Sun decreased by $10.0 \%$ , then what would be the intensity of solar radiation reaching the Earth?

A) $578 \mathrm{~W} / \mathrm{m}^{2}$
B) $752 \mathrm{~W} / \mathrm{m}^{2}$
C) $667 \mathrm{~W} / \mathrm{m}^{2}$
D) $610 \mathrm{~W} / \mathrm{m}^{2}$
E) $879 \mathrm{~W} / \mathrm{m}^{2}$

Question 51

The intensity of solar radiation reaching the Earth is $1,340 \mathrm{~W} / \mathrm{m}^{2}$ when the temperature of the Sun is $5,800 \mathrm{~K}$ . If the temperature of the Sun increased by $10.00 \%$ , then what would be the intensity of solar radiation reaching the earth?

A) $1,828 \mathrm{~W} / \mathrm{m}^{2}$
B) $1,962 \mathrm{~W} / \mathrm{m}^{2}$
C) $2,004 \mathrm{~W} / \mathrm{m}^{2}$
D) $1,492 \mathrm{~W} / \mathrm{m}^{2}$
E) $1,632 \mathrm{~W} / \mathrm{m}^{2}$

Question 52

A $7.5 \mathrm{~kg}$ bowling ball is dropped from the top of a $25 \mathrm{~m}$ tall building. Ignoring air resistance, just before the bowling ball hits the sidewalk below, its kinetic energy is equivalent to how many food Calories? (one food Calorie $=1$ kilocalorie in SI units)

A) 0.44
B) 440
C) 0.22
D) 880
E) 220
F) 0.88

Question 53

A rigid cubic box, $15 \mathrm{~cm}$ on a side, is filled with nitrogen gas $\left(\mathrm{N}_{2}\right)$ at standard temperature and pressure $(0$ ${ }^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ ). The temperature of the box is later raised to $25^{\circ} \mathrm{C}$ . What is the heat input required to perform this act?

A) $157 \mathrm{~J}$
B) $31.4 \mathrm{~J}$
C) $52.3 \mathrm{~J}$
D) $78.2 \mathrm{~J}$
E) $94.1 \mathrm{~J}$
F) $47.1 \mathrm{~J}$

Question 54

A rigid cylindrical container, $15 \mathrm{~cm}$ tall and $15 \mathrm{~cm}$ in radius, is filled with xenon (a monatomic gas) at standard temperature $\left(0{ }^{\circ} \mathrm{C}\right)$ and pressure $(1 \mathrm{~atm})$ . The temperature of the container is later raised to $25^{\circ} \mathrm{C}$ . What is the heat input required to perform this act?

A) $300 \mathrm{~J}$
B) $250 \mathrm{~J}$
C) $150 \mathrm{~J}$
D) $490 \mathrm{~J}$
E) $100 \mathrm{~J}$
F) $160 \mathrm{~J}$

Question 55

A rigid cylindrical container, $15 \mathrm{~cm}$ tall and $15 \mathrm{~cm}$ in radius, is filled with xenon (a monatomic gas) at standard temperature $\left(0{ }^{\circ} \mathrm{C}\right)$ and pressure $(1 \mathrm{~atm})$ . If the heat input to the container is $185 \mathrm{~J}$ , what is the final temperature of the gas?

A) $28^{\circ} \mathrm{C}$
B) $47^{\circ} \mathrm{C}$
C) $9.4^{\circ} \mathrm{C}$
D) $19^{\circ} \mathrm{C}$
E) $16^{\circ} \mathrm{C}$
F) $31^{\circ} \mathrm{C}$

Question 56

A rigid cylinder ( $15 \mathrm{~cm}$ radius, $15 \mathrm{~cm}$ height) contains nitrogen gas $\left(\mathrm{N}_{2}\right)$ at standard temperature and pressure $\left(0{ }^{\circ} \mathrm{C}\right.$ and $\left.1 \mathrm{~atm}\right)$ . What is the total translational kinetic energy of the gas molecules in the cylinder?

A) $0.51 \mathrm{~kJ}$
B) $0.86 \mathrm{~kJ}$
C) $2.7 \mathrm{~kJ}$
D) $1.6 \mathrm{~kJ}$

Question 57

A rigid cylinder ( $15 \mathrm{~cm}$ radius, $15 \mathrm{~cm}$ height) contains nitrogen gas $\left(\mathrm{N}_{2}\right)$ at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $\left.1 \mathrm{~atm}\right)$ . What heat input is required to increase the average translational kinetic energy of the nitrogen molecules by $15 \%$ ?

A) $77 \mathrm{~J}$
B) $260 \mathrm{~J}$
C) $130 \mathrm{~J}$
D) $86 \mathrm{~J}$
E) $51 \mathrm{~J}$
F) $403 \mathrm{~J}$

Question 58

A circular window in the wall of a home has a diameter of $25 \mathrm{~cm}$ and is made of a single pane of glass 0.30 $\mathrm{cm}$ thick. The thermal conductivity for the glass is $0.63 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$ . If $1.6 \mathrm{~kJ}$ of heat is lost through the window in $12 \mathrm{~s}$ , and if inside the house the temperature is $20^{\circ} \mathrm{C}$ , what is the outside temperature?

A) $17^{\circ} \mathrm{C}$
B) $-12{ }^{\circ} \mathrm{C}$
C) $18^{\circ} \mathrm{C}$
D) $-17^{\circ} \mathrm{C}$
E) $7.1^{\circ} \mathrm{C}$