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 = 150 MW

A power plant delivers a net power output of 150 MW with a thermal efficiency of 38%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 150 MWη = 38%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 1900 kJQL​ = 1140 kJW

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1140 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1900 kJQL = 1140 kJ
η = %
3.Medium
TH​ = 450 °CTL​ = 10 °CEQH​QL​η = 37%

A heat engine receives heat from a source at 450 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 37%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 450 °CTL = 10 °Cη = 37%
ηII = %
4.Medium
TH​ = 400 °CTL​ = 30 °CEQH​ = 2400 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 30 °C. It takes in 2400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 30 °CQH = 2400 kJ
Wmax = kJ
5.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 7.5 kWQ̇L​Ẇ = ?

A heat pump delivers 7.5 kW of heat to a heating system at 20 °C, taking heat from a source at 7 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = 7 °CηII = 30%Q̇H = 7.5 kW
Ẇ = kW
6.Hard
TH​ = 30 °CTL​ = -18 °CRQ̇H​Q̇L​ = 3 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 30 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -18 °CQ̇L = 3 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 244.7 MW
  2. 2. η = 40 %
  3. 3. ηII = 60.81 %
  4. 4. Wmax = 1319 kJ
  5. 5. Ẇ = 1.109 kW
  6. 6. Ẇmin = 0.5644 kW

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