Worksheet: Heat Pumps

In this worksheet, we will practice comparing the work done by heat pumps with reservoirs at different temperatures and calculating their performance coefficients.

Q1:

A refrigerator connects reservoirs with temperatures of 260 K and 320 K. What is the change in the temperature of the low-temperature reservoir that results in the work required to cool the low-temperature reservoir being halved? Give your answer to three significant figures.

Q2:

A refrigerator connects reservoirs with temperatures of 270 K and 360 K. What is the change in temperature of the high-temperature reservoir that results in the work required to cool the low-temperature reservoir being halved? Answer to three significant figures.

Q3:

A heat pump heats a high-temperature reservoir with a temperature of 35∘C by 7.5 J for each joule of work that it does. The pump connects the reservoir to a low-temperature reservoir. What is the temperature of the low-temperature reservoir? Answer in degrees Celsius to three significant figures.

Q4:

Heat pumps and refrigerators are very similar to each other, consisting of the same basic components. However, they are not modeled in exactly the same way as each other.

Which of the following statements correctly explains the similarities between a heat pump and a refrigerator?

  • AA heat pump and a refrigerator both have the same efficiency when transferring internal energy between two reservoirs with the same two temperatures, π‘‡οŠ§ and π‘‡οŠ¨.
  • BA heat pump and a refrigerator both transfer internal energy from a low-temperature reservoir to a high-temperature reservoir.

Which of the following statements correctly explains the differences between a heat pump and a refrigerator?

  • AA heat pump transfers internal energy from a high-temperature reservoir to a low-temperature reservoir, whereas a refrigerator transfers internal energy from a low-temperature reservoir to a high-temperature reservoir.
  • BThe efficiency of a heat pump depends on how much work it does to add internal energy to a high-temperature reservoir, whereas the efficiency of a refrigerator depends on how much work it does to remove internal energy from a low-temperature reservoir.

Q5:

A heat pump is represented in the diagram, showing the quantities associated with its operation. If the value of π‘Š, the work done by the pump, is zero, what is the relationship between the magnitudes of 𝑄in and 𝑄out? Assume that the reservoirs are not at the same temperature as each other.

  • A𝑄×𝑄=1outin
  • B𝑄<𝑄inout
  • C𝑄>𝑄inout
  • D𝑄=𝑄inout
  • E𝑄𝑄=1outin

Q6:

A heat pump is represented in the diagram, showing the quantities associated with its operation. Which of the following formulas most correctly represents the relationship between 𝑄in, 𝑄out, and π‘Š?

  • Aπ‘„βˆ’π‘„=π‘Šoutin
  • Bπ‘„βˆ’π‘„=π‘Šinout
  • C𝑄𝑄=π‘Šinout
  • D𝑄+𝑄=π‘Šinout
  • E𝑄𝑄=π‘Šoutin

Q7:

A heat pump heats a high-temperature reservoir by 4.5 J for each joule of work that it does. The pump connects a low-temperature reservoir with a temperature of –2.5∘C to the high-temperature reservoir. What is the temperature of the high-temperature reservoir? Answer in degrees Celsius to three significant figures.

Q8:

A heat pump connects reservoirs with temperatures of 280 K and 310 K. A refrigerator also connects reservoirs with these temperatures. The coefficients of performance of the heat pump and the refrigerator are calculated differently.

What is the ratio of the heating of the high-temperature reservoir to the work done by the heat pump? Answer to two significant figures.

What is the ratio of the cooling of the low-temperature reservoir to the work done by the refrigerator? Answer to two significant figures.

Q9:

The diagram shows the circulation of a coolant fluid through a refrigerator, showing four specific stages at which changes occur to the fluid.

At what stages does the coolant change state?

  • AII and IV
  • BIV and I
  • CIII and I
  • DIII and IV
  • EII and I

Which component’s action increases the temperature of the coolant?

  • ACompressor
  • BExpansion valve

Which component’s action decreases the temperature of the coolant?

  • ACompressor
  • BExpansion valve

Q10:

The graph shows the changes in the coefficients of performance of two heat pumps with changes in the temperatures of their low-temperature reservoirs. The pumps represented by the blue points and by the orange points heat high-temperature reservoirs that are at temperatures π‘‡οŠ§ and π‘‡οŠ¨ respectively. Both π‘‡οŠ§ and π‘‡οŠ¨ are greater than 335 K. Which temperature is greater?

  • Aπ‘‡οŠ§
  • Bπ‘‡οŠ¨

Q11:

The diagram shows the circulation of a coolant fluid through a refrigerator, showing four specific stages at which changes occur to the fluid.

In stage I, is the net work done on the gas positive, negative, or zero?

  • ANegative
  • BPositive
  • CZero

In stage I, is the net heating of the gas positive, negative, or zero?

  • ANegative
  • BZero
  • CPositive

In stage II, is the net work done on the gas positive, negative, or zero?

  • AZero
  • BPositive
  • CNegative

In stage II, is the net heating of the gas positive, negative, or zero?

  • AZero
  • BNegative
  • CPositive

In stage III, is the net work done on the gas positive, negative, or zero?

  • APositive
  • BNegative
  • CZero

In stage III, is the net heating of the gas positive, negative, or zero?

  • AZero
  • BPositive
  • CNegative

In stage IV, is the net work done on the gas positive, negative, or zero?

  • AZero
  • BNegative
  • CPositive

In stage IV, is the net heating of the gas positive, negative, or zero?

  • AZero
  • BNegative
  • CPositive

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