Heat engines & refrigerators worksheet with answers

Free printable Heat engines & refrigerators worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A heat engine takes in 1400 kJ of heat from a hot reservoir and rejects 980 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

Q_H = 1400 kJQ_L = 980 kJ

W = kJ

2.Easy

A heat engine takes in 4600 kJ of heat from a hot reservoir and rejects 3220 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 4600 kJQ_L = 3220 kJ

η = %

3.Medium

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 47%. Find its second-law efficiency η_II, the ratio of the actual efficiency to the Carnot efficiency.

T_H = 800 °CT_L = 25 °Cη = 47%

η_II = %

4.Medium

A reversible (Carnot) heat engine takes in 2600 kJ of heat from a reservoir at 425 °C and rejects 1185 kJ per cycle. Find the temperature T_L of the cold reservoir in °C.

T_H = 425 °CQ_H = 2600 kJQ_L = 1185 kJ

T_L = °C

5.Hard

A heat pump keeps a house at 20 °C while it is 7 °C outside, delivering 13 kW of heat to the house. Find the minimum power input Ẇ_min.

T_H = 20 °CT_L = 7 °CQ̇_H = 13 kW

Ẇ_min = kW

6.Hard

A heat pump delivers 6.5 kW of heat to a heating system at 22 °C, taking heat from a source at 0 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

T_H = 22 °CT_L = 0 °Cη_II = 30%Q̇_H = 6.5 kW

Ẇ = kW

Answer key

1. W = 420 kJ
2. η = 30 %
3. η_II = 65.08 %
4. T_L = 45.05 °C
5. Ẇ_min = 0.5765 kW
6. Ẇ = 1.615 kW

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