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​ = 3700 kJQL​ = 2775 kJW = ?

A heat engine takes in 3700 kJ of heat from a hot reservoir and rejects 2775 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3700 kJQL = 2775 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 33%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 300 MWη = 33%
Q̇L = MW
3.Medium
TH​ = 800 °CTL​ = 10 °CEQH​QL​η = 44%

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 44%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 800 °CTL = 10 °Cη = 44%
ηII = %
4.Medium
TH​ = 425 °CTL​ = 10 °CEQH​ = 2600 kJQL​W = ?

A heat engine works between a hot reservoir at 425 °C and a cold reservoir at 10 °C. It takes in 2600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 425 °CTL = 10 °CQH = 2600 kJ
Wmax = kJ
5.Hard
600 °CTm​ = ?40 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 600 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 40 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 600 °CTL = 40 °C
Tm = °C
6.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -5 °C outside, delivering 4 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -5 °CQ̇H = 4 kW
Ẇmin = kW

Answer key

  1. 1. W = 925 kJ
  2. 2. Q̇L = 609.1 MW
  3. 3. ηII = 59.77 %
  4. 4. Wmax = 1546 kJ
  5. 5. Tm = 249.8 °C
  6. 6. Ẇmin = 0.3536 kW

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