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 2000 kJ of heat from a hot reservoir and rejects 1500 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 2000 kJQ_L = 1500 kJ

η = %

2.Easy

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2145 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

Q_H = 3900 kJQ_L = 2145 kJ

W = kJ

3.Medium

A reversible (Carnot) heat engine takes in 3800 kJ of heat from a reservoir at 450 °C and rejects 1462 kJ per cycle. Find the temperature T_L of the cold reservoir in °C.

T_H = 450 °CQ_H = 3800 kJQ_L = 1462 kJ

T_L = °C

4.Medium

A reversible (Carnot) heat engine takes in 1400 kJ of heat from a reservoir at 525 °C and rejects 488 kJ per cycle. Find the temperature T_L of the cold reservoir in °C.

T_H = 525 °CQ_H = 1400 kJQ_L = 488 kJ

T_L = °C

5.Hard

A refrigerator keeps its cold space at 2 °C in a kitchen at 30 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇ_min.

T_H = 30 °CT_L = 2 °CQ̇_L = 4 kW

Ẇ_min = kW

6.Hard

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 14 kW of heat to the house. Find the highest possible coefficient of performance COP_max.

T_H = 20 °CT_L = 2 °CQ̇_H = 14 kW

COP_max =

Answer key

1. η = 25 %
2. W = 1755 kJ
3. T_L = 5.072 °C
4. T_L = 5.062 °C
5. Ẇ_min = 0.4071 kW
6. COP_max = 16.29

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