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​ = 900 kJQL​ = 720 kJW

A heat engine takes in 900 kJ of heat from a hot reservoir and rejects 720 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 900 kJQL = 720 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 40%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 300 MWη = 40%
Q̇L = MW
3.Medium
TH​ = 40 °CTL​ = 0 °CRQ̇H​ = ?Q̇L​ = 2.5 kWẆ

A reversible refrigerator keeps a cold room at 0 °C by removing 2.5 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = 0 °CTH = 40 °CQ̇L = 2.5 kW
Q̇H = kW
4.Medium
TH​ = 575 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 575 °CTL = 30 °C
ηmax = %
5.Hard
TH​ = 650 °CT0​ = 25 °CTL​ = -15 °CERWQ̇H​ = 80 kWQ̇L​ = ?

A Carnot heat engine receives 80 kW of heat from a source at 650 °C and rejects heat to the surroundings at 25 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 25 °CTL = -15 °CQ̇H = 80 kW
Q̇L = kW
6.Hard
TH​ = 900 °CTL​ = 10 °CEQH​ = 4600 kJQL​ = 2484 kJW = 2116 kJ

A heat engine takes in 4600 kJ of heat from a reservoir at 900 °C, produces 2116 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 900 °CTL = 10 °CQH = 4600 kJW = 2116 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 20 %
  2. 2. Q̇L = 450 MW
  3. 3. Q̇H = 2.866 kW
  4. 4. ηmax = 64.26 %
  5. 5. Q̇L = 349.6 kW
  6. 6. Sgen = 4.852 kJ/K

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