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​ = 3000 kJQL​ = 1950 kJW

A heat engine takes in 3000 kJ of heat from a hot reservoir and rejects 1950 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3000 kJQL = 1950 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 30%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 50 MWη = 30%
Q̇L = MW
3.Medium
TH​ = 400 °CTL​ = 30 °CEQH​ = 2000 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 30 °C. It takes in 2000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 30 °CQH = 2000 kJ
Wmax = kJ
4.Medium
TH​ = 700 °CTL​ = 10 °CEQH​QL​η = 50%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 50%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 10 °Cη = 50%
ηII = %
5.Hard
1050 °CTm​ = ?15 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 1050 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 15 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 1050 °CTL = 15 °C
Tm = °C
6.Hard
TH​ = 22 °CTL​ = -5 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -5 °C outside, delivering 9 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -5 °CQ̇H = 9 kW
Ẇmin = kW

Answer key

  1. 1. η = 35 %
  2. 2. Q̇L = 116.7 MW
  3. 3. Wmax = 1099 kJ
  4. 4. ηII = 70.52 %
  5. 5. Tm = 344.3 °C
  6. 6. Ẇmin = 0.8233 kW

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