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 = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 25%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 600 MWη = 25%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 1100 kJQL​ = 770 kJW

A heat engine takes in 1100 kJ of heat from a hot reservoir and rejects 770 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1100 kJQL = 770 kJ
η = %
3.Medium
TH​ = 600 °CTL​ = 30 °CEQH​QL​η = 39%

A heat engine receives heat from a source at 600 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 39%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 600 °CTL = 30 °Cη = 39%
ηII = %
4.Medium
TH​ = 30 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 7 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 7 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 30 °CQ̇L = 7 kW
Q̇H = kW
5.Hard
TH​ = 35 °CTL​ = 2 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at 2 °C in a kitchen at 35 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = 2 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 800 °CTL​ = 25 °CEQH​ = 3800 kJQL​ = 2432 kJW = 1368 kJ

A heat engine takes in 3800 kJ of heat from a reservoir at 800 °C, produces 1368 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 800 °CTL = 25 °CQH = 3800 kJW = 1368 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇H = 2400 MW
  2. 2. η = 30 %
  3. 3. ηII = 59.74 %
  4. 4. Q̇H = 8.317 kW
  5. 5. Ẇmin = 0.2399 kW
  6. 6. Sgen = 4.616 kJ/K

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