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 600 kJ of heat from a hot reservoir and rejects 390 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 600 kJQ_L = 390 kJ

η = %

2.Easy

A heat engine takes in 1700 kJ of heat from a hot reservoir and rejects 935 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

Q_H = 1700 kJQ_L = 935 kJ

W = kJ

3.Medium

A reversible (Carnot) heat engine takes in 3400 kJ of heat from a reservoir at 775 °C and rejects 1032 kJ per cycle. Find the temperature T_L of the cold reservoir in °C.

T_H = 775 °CQ_H = 3400 kJQ_L = 1032 kJ

T_L = °C

4.Medium

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency η_max.

T_H = 375 °CT_L = 15 °C

η_max = %

5.Hard

A heat pump delivers 13.5 kW of heat to a heating system at 45 °C, taking heat from a source at 2 °C. Its actual COP is 40% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

T_H = 45 °CT_L = 2 °Cη_II = 40%Q̇_H = 13.5 kW

Ẇ = kW

6.Hard

Two Carnot engines work in series. Engine A receives heat from a reservoir at 950 °C and rejects heat to an intermediate reservoir at temperature T_m. Engine B takes all that heat and rejects heat to a reservoir at 30 °C. Both engines have the same thermal efficiency. Find T_m in °C.

T_H = 950 °CT_L = 30 °C

T_m = °C

Answer key

1. η = 35 %
2. W = 765 kJ
3. T_L = 44.99 °C
4. η_max = 55.54 %
5. Ẇ = 4.562 kW
6. T_m = 335.8 °C

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