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
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 50%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 50 MWη = 50%
Q̇H = MW
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 1.82 kWẆ = 0.7 kW

A refrigerator removes heat from its cold space at a rate of 1.82 kW while its compressor uses 0.7 kW of power. Find its coefficient of performance COPR.

Q̇L = 1.82 kWẆ = 0.7 kW
COPR =
3.Medium
TH​ = 750 °CTL​ = 15 °CEQH​QL​η = 47%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 47%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 15 °Cη = 47%
ηII = %
4.Medium
TH​ = 450 °CTL​ = 40 °CEQH​ = 900 kJQL​W = ?

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 40 °C. It takes in 900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 450 °CTL = 40 °CQH = 900 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 8 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 8 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 5 °CQ̇H = 8 kW
COPmax =
6.Hard
950 °CTm​ = ?40 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 950 °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 = 950 °CTL = 40 °C
Tm = °C

Answer key

  1. 1. Q̇H = 100 MW
  2. 2. COPR = 2.6
  3. 3. ηII = 65.43 %
  4. 4. Wmax = 510.3 kJ
  5. 5. COPmax = 17.36
  6. 6. Tm = 345.7 °C

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