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 = 100 MW

A power plant delivers a net power output of 100 MW with a thermal efficiency of 33%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 100 MWη = 33%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 1800 kJQL​ = 1170 kJW

A heat engine takes in 1800 kJ of heat from a hot reservoir and rejects 1170 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1800 kJQL = 1170 kJ
η = %
3.Medium
TH​ = 800 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 450 °CTL​ = 10 °CEQH​ = 800 kJQL​W = ?

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 10 °C. It takes in 800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 450 °CTL = 10 °CQH = 800 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = 0 °CHPQ̇H​ = 9 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 0 °C outside, delivering 9 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 0 °CQ̇H = 9 kW
COPmax =
6.Hard
TH​ = 32 °CTL​ = -10 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 32 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -10 °CQ̇L = 4 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 203 MW
  2. 2. η = 35 %
  3. 3. ηmax = 72.68 %
  4. 4. Wmax = 486.8 kJ
  5. 5. COPmax = 13.42
  6. 6. Ẇmin = 0.6384 kW

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