1.Easy
A heat engine takes in 1600 kJ of heat from a hot reservoir and rejects 1200 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.
QH = 1600 kJQL = 1200 kJ
η = %
Heat engines & refrigerators worksheet with answers
2.Easy
A heat engine takes in 4600 kJ of heat from a hot reservoir and rejects 3450 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.
QH = 4600 kJQL = 3450 kJ
W = kJ
3.Medium
A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 48%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.
TH = 700 °CTL = 30 °Cη = 48%
ηII = %
4.Medium
A reversible refrigerator keeps a cold room at -10 °C by removing 9.5 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.
TL = -10 °CTH = 20 °CQ̇L = 9.5 kW
Q̇H = kW
5.Hard
A Carnot heat engine receives 80 kW of heat from a source at 950 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at 0 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.
TH = 950 °CT0 = 30 °CTL = 0 °CQ̇H = 80 kW
Q̇L = kW
6.Hard
A refrigerator keeps its cold space at -18 °C in a kitchen at 32 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇmin.
TH = 32 °CTL = -18 °CQ̇L = 3 kW
Ẇmin = kW
Answer key
- 1. η = 25 %
- 2. W = 1150 kJ
- 3. ηII = 69.72 %
- 4. Q̇H = 10.58 kW
- 5. Q̇L = 547.9 kW
- 6. Ẇmin = 0.5879 kW
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