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 = 500 MW

A power plant delivers a net power output of 500 MW with a thermal efficiency of 42%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 500 MWη = 42%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 1600 kJQL​ = 1120 kJW = ?

A heat engine takes in 1600 kJ of heat from a hot reservoir and rejects 1120 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1600 kJQL = 1120 kJ
W = kJ
3.Medium
TH​ = 40 °CTL​ = -25 °CRQ̇H​ = ?Q̇L​ = 7.5 kWẆ

A reversible refrigerator keeps a cold room at -25 °C by removing 7.5 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = -25 °CTH = 40 °CQ̇L = 7.5 kW
Q̇H = kW
4.Medium
TH​ = 550 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 550 °CTL = 20 °C
ηmax = %
5.Hard
TH​ = 600 °CT0​ = 25 °CTL​ = -15 °CERWQ̇H​ = 200 kWQ̇L​ = ?

A Carnot heat engine receives 200 kW of heat from a source at 600 °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 = 600 °CT0 = 25 °CTL = -15 °CQ̇H = 200 kW
Q̇L = kW
6.Hard
TH​ = 500 °CT0​ = 27 °CTL​ = -25 °CERWQ̇H​ = 130 kWQ̇L​ = ?

A Carnot heat engine receives 130 kW of heat from a source at 500 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -25 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 500 °CT0 = 27 °CTL = -25 °CQ̇H = 130 kW
Q̇L = kW

Answer key

  1. 1. Q̇L = 690.5 MW
  2. 2. W = 480 kJ
  3. 3. Q̇H = 9.465 kW
  4. 4. ηmax = 64.39 %
  5. 5. Q̇L = 850 kW
  6. 6. Q̇L = 379.5 kW

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