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 = 1000 MW

A power plant delivers a net power output of 1000 MW with a thermal efficiency of 33%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 1000 MWη = 33%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 1100 kJQL​ = 880 kJW = ?

A heat engine takes in 1100 kJ of heat from a hot reservoir and rejects 880 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1100 kJQL = 880 kJ
W = kJ
3.Medium
TH​ = 35 °CTL​ = -30 °CRQ̇H​ = ?Q̇L​ = 1 kWẆ

A reversible refrigerator keeps a cold room at -30 °C by removing 1 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = -30 °CTH = 35 °CQ̇L = 1 kW
Q̇H = kW
4.Medium
TH​ = 450 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 450 °CTL = 10 °C
ηmax = %
5.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -10 °CQ̇H = 7 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = 0 °CHPQ̇H​ = 9 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is 0 °C outside, delivering 9 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = 0 °CQ̇H = 9 kW
COPmax =

Answer key

  1. 1. Q̇L = 2030 MW
  2. 2. W = 220 kJ
  3. 3. Q̇H = 1.267 kW
  4. 4. ηmax = 60.84 %
  5. 5. Ẇmin = 0.7164 kW
  6. 6. COPmax = 14.01

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