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
hot reservoircold reservoirEQH​ = 1100 kJQL​ = 715 kJW = ?

A heat engine takes in 1100 kJ of heat from a hot reservoir and rejects 715 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1100 kJQL = 715 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 42%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 300 MWη = 42%
Q̇H = MW
3.Medium
TH​ = 350 °CTL​ = 35 °CEQH​QL​η = 25%

A heat engine receives heat from a source at 350 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 25%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 350 °CTL = 35 °Cη = 25%
ηII = %
4.Medium
TH​ = 20 °CTL​ = -30 °CRQ̇H​ = ?Q̇L​ = 8.5 kWẆ

A reversible refrigerator keeps a cold room at -30 °C by removing 8.5 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = -30 °CTH = 20 °CQ̇L = 8.5 kW
Q̇H = kW
5.Hard
TH​ = 35 °CTL​ = -20 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 35 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = -20 °CQ̇L = 1.5 kW
Ẇmin = kW
6.Hard
TH​ = 20 °CTL​ = 5 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 5 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 5 °CQ̇H = 8 kW
Ẇmin = kW

Answer key

  1. 1. W = 385 kJ
  2. 2. Q̇H = 714.3 MW
  3. 3. ηII = 49.46 %
  4. 4. Q̇H = 10.25 kW
  5. 5. Ẇmin = 0.3259 kW
  6. 6. Ẇmin = 0.4093 kW

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