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 = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 50%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 600 MWη = 50%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 2200 kJQL​ = 1650 kJW

A heat engine takes in 2200 kJ of heat from a hot reservoir and rejects 1650 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2200 kJQL = 1650 kJ
η = %
3.Medium
TH​ = 725 °CTL​ = ?EQH​ = 700 kJQL​ = 192 kJW

A reversible (Carnot) heat engine takes in 700 kJ of heat from a reservoir at 725 °C and rejects 192 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 725 °CQH = 700 kJQL = 192 kJ
TL = °C
4.Medium
TH​ = 20 °CTL​ = 4 °CRQ̇H​ = ?Q̇L​ = 8 kWẆ

A reversible refrigerator keeps a cold room at 4 °C by removing 8 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = 4 °CTH = 20 °CQ̇L = 8 kW
Q̇H = kW
5.Hard
TH​ = 20 °CTL​ = 2 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 2 °CQ̇H = 5 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = 0 °CHPQ̇H​ = 15 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is 0 °C outside, delivering 15 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = 0 °CQ̇H = 15 kW
COPmax =

Answer key

  1. 1. Q̇L = 600 MW
  2. 2. η = 25 %
  3. 3. TL = 0.6283 °C
  4. 4. Q̇H = 8.462 kW
  5. 5. Ẇmin = 0.307 kW
  6. 6. COPmax = 14.01

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