1.Easy
A refrigerator removes heat from its cold space at a rate of 2 kW while its compressor uses 0.5 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.
Q̇L = 2 kWẆ = 0.5 kW
Q̇H = kW
Heat engines & refrigerators worksheet with answers
2.Easy
A heat engine takes in 5000 kJ of heat from a hot reservoir and rejects 3500 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.
QH = 5000 kJQL = 3500 kJ
η = %
3.Medium
A reversible (Carnot) heat engine takes in 3600 kJ of heat from a reservoir at 700 °C and rejects 1177 kJ per cycle. Find the temperature TL of the cold reservoir in °C.
TH = 700 °CQH = 3600 kJQL = 1177 kJ
TL = °C
4.Medium
A reversible refrigerator keeps a cold room at 2 °C by removing 4.5 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.
TL = 2 °CTH = 40 °CQ̇L = 4.5 kW
Q̇H = kW
5.Hard
A refrigerator keeps its cold space at -25 °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 = -25 °CQ̇L = 3 kW
Ẇmin = kW
6.Hard
A Carnot heat engine receives 30 kW of heat from a source at 550 °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 -30 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.
TH = 550 °CT0 = 30 °CTL = -30 °CQ̇H = 30 kW
Q̇L = kW
Answer key
- 1. Q̇H = 2.5 kW
- 2. η = 30 %
- 3. TL = 45.02 °C
- 4. Q̇H = 5.121 kW
- 5. Ẇmin = 0.6891 kW
- 6. Q̇L = 76.8 kW
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