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​ = 1900 kJQL​ = 1235 kJW = ?

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1235 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1900 kJQL = 1235 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 35%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 600 MWη = 35%
Q̇L = MW
3.Medium
TH​ = 625 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 625 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 325 °CTL​ = 10 °CEQH​ = 2500 kJQL​W = ?

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 10 °C. It takes in 2500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 325 °CTL = 10 °CQH = 2500 kJ
Wmax = kJ
5.Hard
TH​ = 450 °CTL​ = 20 °CEQH​ = 2300 kJQL​ = 1610 kJW = 690 kJ

A heat engine takes in 2300 kJ of heat from a reservoir at 450 °C, produces 690 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 450 °CTL = 20 °CQH = 2300 kJW = 690 kJ
Sgen = kJ/K
6.Hard
TH​ = 25 °CTL​ = -20 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 25 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = -20 °CQ̇L = 4 kW
Ẇmin = kW

Answer key

  1. 1. W = 665 kJ
  2. 2. Q̇L = 1114 MW
  3. 3. ηmax = 67.36 %
  4. 4. Wmax = 1317 kJ
  5. 5. Sgen = 2.312 kJ/K
  6. 6. Ẇmin = 0.711 kW

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