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​ = 4400 kJQL​ = 3300 kJW = ?

A heat engine takes in 4400 kJ of heat from a hot reservoir and rejects 3300 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4400 kJQL = 3300 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 150 MW

A power plant delivers a net power output of 150 MW with a thermal efficiency of 33%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 150 MWη = 33%
Q̇L = MW
3.Medium
TH​ = 250 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 250 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 28 °CTL​ = -20 °CRQ̇H​ = ?Q̇L​ = 6.5 kWẆ

A reversible refrigerator keeps a cold room at -20 °C by removing 6.5 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = -20 °CTH = 28 °CQ̇L = 6.5 kW
Q̇H = kW
5.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 15 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -10 °CQ̇H = 15 kW
Ẇmin = kW
6.Hard
TH​ = 450 °CT0​ = 25 °CTL​ = -15 °CERWQ̇H​ = 130 kWQ̇L​ = ?

A Carnot heat engine receives 130 kW of heat from a source at 450 °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 = 450 °CT0 = 25 °CTL = -15 °CQ̇H = 130 kW
Q̇L = kW

Answer key

  1. 1. W = 1100 kJ
  2. 2. Q̇L = 304.5 MW
  3. 3. ηmax = 42.05 %
  4. 4. Q̇H = 7.732 kW
  5. 5. Ẇmin = 1.535 kW
  6. 6. Q̇L = 493.1 kW

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