1.Easy
A heat pump with a coefficient of performance of 4.9 delivers 15 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.
COPHP = 4.9Q̇H = 15 kW
Q̇L = kW
Heat engines & refrigerators worksheet with answers
2.Easy
A heat engine takes in 3000 kJ of heat from a hot reservoir and rejects 2250 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.
QH = 3000 kJQL = 2250 kJ
η = %
3.Medium
A reversible refrigerator keeps a cold room at -20 °C by removing 5 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.
TL = -20 °CTH = 20 °CQ̇L = 5 kW
Q̇H = kW
4.Medium
A reversible refrigerator keeps a cold room at 4 °C by removing 8.5 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.
TL = 4 °CTH = 40 °CQ̇L = 8.5 kW
Q̇H = kW
5.Hard
A Carnot heat engine receives 30 kW of heat from a source at 700 °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 = 700 °CT0 = 30 °CTL = -30 °CQ̇H = 30 kW
Q̇L = kW
6.Hard
A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.
TH = 20 °CTL = -10 °CQ̇H = 8 kW
Ẇmin = kW
Answer key
- 1. Q̇L = 11.94 kW
- 2. η = 25 %
- 3. Q̇H = 5.79 kW
- 4. Q̇H = 9.604 kW
- 5. Q̇L = 83.7 kW
- 6. Ẇmin = 0.8187 kW
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