Q: A 100 g sample of water at $100\ ^\circ\mathrm{C}$ is cooled to $40\ ^\circ\mathrm{C}$. How much heat is released? ($c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$)

$Q = 100 \times 4.18 \times (100 - 40) = 25,080\ \mathrm{J}$

Q: A hospital uses ice packs to cool a patient. If each ice pack contains 250 g of ice at $0\ ^\circ\mathrm{C}$, how much heat is absorbed by one ice pack as it melts completely? ($L_f = 334\ \mathrm{J/g}$)

$Q = 250 \times 334 = 83,500\ \mathrm{J}$

Q: A scientist wants to condense 10 g of steam at $100\ ^\circ\mathrm{C}$ to liquid water at $40\ ^\circ\mathrm{C}$. How much heat must be removed? ($c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_v = 2260\ \mathrm{J/g}$)

$Q = 10 \times 2260 + 10 \times 4.18 \times (100 - 40) = 22,600 + 2,508 = 25,108\ \mathrm{J}$

Question 1

A 160 g block of ice at $0\ ^\circ\mathrm{C}$ is mixed with a certain mass of steam at $100\ ^\circ\mathrm{C}$ in a thermally insulated container. What is the minimum mass of steam required to produce liquid water at $40\ ^\circ\mathrm{C}$? (Assume $c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_f = 334\ \mathrm{J/g}$, $L_v = 2260\ \mathrm{J/g}$)

Accepted Answer

32 g

Question 2

100 g of ice at $0\ ^\circ\mathrm{C}$ is mixed with 100 g of water at $70\ ^\circ\mathrm{C}$ in a thermally insulated container. What is the final temperature of the mixture? (Assume $c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_f = 334\ \mathrm{J/g}$)

Accepted Answer

36 $^\circ$C

Question 3

Which of the following best describes the process when steam at $100\ ^\circ\mathrm{C}$ is added to ice at $0\ ^\circ\mathrm{C}$ in a thermally insulated container?

Accepted Answer

Steam condenses, releases latent heat, and then cools down; ice melts, absorbs latent heat, and then warms up.

Question 4

If 50 g of ice at $0\ ^\circ\mathrm{C}$ is mixed with 200 g of water at $30\ ^\circ\mathrm{C}$, what is the final temperature of the mixture? (Assume $c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_f = 334\ \mathrm{J/g}$)

Accepted Answer

18 $^\circ$C

Question 5

A student mixes 80 g of ice at $0\ ^\circ\mathrm{C}$ with 120 g of water at $50\ ^\circ\mathrm{C}$. Calculate the amount of ice that remains after thermal equilibrium is reached. (Assume $c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_f = 334\ \mathrm{J/g}$)

Accepted Answer

0 g

Question 6

Which equation correctly represents the heat gained or lost by a substance undergoing a temperature change without a phase change?

Accepted Answer

$Q = mc\Delta T$

Question 7

A 100 g sample of water at $100\ ^\circ\mathrm{C}$ is cooled to $40\ ^\circ\mathrm{C}$. How much heat is released? ($c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$)

Accepted Answer

$Q = 100 	imes 4.18 	imes (100 - 40) = 25,080\ \mathrm{J}$

Question 8

Which of the following statements about latent heat is correct?

Accepted Answer

Latent heat is the energy required for a phase change at constant temperature.

Question 9

A hospital uses ice packs to cool a patient. If each ice pack contains 250 g of ice at $0\ ^\circ\mathrm{C}$, how much heat is absorbed by one ice pack as it melts completely? ($L_f = 334\ \mathrm{J/g}$)

Accepted Answer

$Q = 250 	imes 334 = 83,500\ \mathrm{J}$

Question 10

A chef wants to quickly cool 500 g of soup at $80\ ^\circ\mathrm{C}$ to $40\ ^\circ\mathrm{C}$ by adding ice at $0\ ^\circ\mathrm{C}$. What mass of ice is needed? ($c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_f = 334\ \mathrm{J/g}$)

Accepted Answer

31.3 g

Question 11

Which of the following best explains why the temperature of a mixture of ice and water remains at $0\ ^\circ\mathrm{C}$ until all the ice melts?

Accepted Answer

The heat added is used for the phase change, not for increasing temperature.

Question 12

A 200 g sample of water at $20\ ^\circ\mathrm{C}$ is mixed with 100 g of water at $80\ ^\circ\mathrm{C}$. What is the final temperature of the mixture? ($c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$)

Accepted Answer

40 $^\circ$C

Question 13

Which of the following is the correct energy balance equation for mixing ice at $0\ ^\circ\mathrm{C}$ with water at $T_{hot}$ in a thermally insulated container?

Accepted Answer

$m_{ice}L_f + m_{ice}c_{water}(T_f - 0) = m_{water}c_{water}(T_{hot} - T_f)$

Question 14

A scientist wants to condense 10 g of steam at $100\ ^\circ\mathrm{C}$ to liquid water at $40\ ^\circ\mathrm{C}$. How much heat must be removed? ($c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_v = 2260\ \mathrm{J/g}$)

Accepted Answer

$Q = 10 	imes 2260 + 10 	imes 4.18 	imes (100 - 40) = 22,600 + 2,508 = 25,108\ \mathrm{J}$

Question 15

Which of the following is NOT a correct application of the principle of conservation of energy in calorimetry?

Accepted Answer

Heat is created during the mixing process.

Question 16

A beverage company wants to cool 1 kg of soda from $25\ ^\circ\mathrm{C}$ to $5\ ^\circ\mathrm{C}$ using ice at $0\ ^\circ\mathrm{C}$. What mass of ice is required? ($c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_f = 334\ \mathrm{J/g}$)

Accepted Answer

62.6 g

Question 17

Which of the following best describes the role of specific heat capacity in temperature change calculations?

Accepted Answer

It determines the amount of heat required to change the temperature of a unit mass by one degree.

Question 18

A 150 g sample of water at $60\ ^\circ\mathrm{C}$ is mixed with 50 g of ice at $0\ ^\circ\mathrm{C}$. What is the final temperature of the mixture? ($c_{water} = 4.18\ \mathrm{J/g\cdot ^\circ C}$, $L_f = 334\ \mathrm{J/g}$)

Accepted Answer

20 $^\circ$C

Thermal Energy and Calorimetry: Phase Changes and Heat Transfer

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