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​ = 1800 kJQL​ = 990 kJW = ?

A heat engine takes in 1800 kJ of heat from a hot reservoir and rejects 990 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1800 kJQL = 990 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 300 MWη = 25%
Q̇L = MW
3.Medium
TH​ = 650 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 650 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 28 °CTL​ = 2 °CRQ̇H​ = ?Q̇L​ = 6 kWẆ

A reversible refrigerator keeps a cold room at 2 °C by removing 6 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = 2 °CTH = 28 °CQ̇L = 6 kW
Q̇H = kW
5.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 14 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 14 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = -10 °CQ̇H = 14 kW
COPmax =
6.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 7 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 7 °CQ̇H = 8 kW
Ẇmin = kW

Answer key

  1. 1. W = 810 kJ
  2. 2. Q̇L = 900 MW
  3. 3. ηmax = 67.16 %
  4. 4. Q̇H = 6.567 kW
  5. 5. COPmax = 9.772
  6. 6. Ẇmin = 0.3808 kW

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