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 = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 30%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 3100 kJQL​ = 2325 kJW

A heat engine takes in 3100 kJ of heat from a hot reservoir and rejects 2325 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3100 kJQL = 2325 kJ
η = %
3.Medium
TH​ = 500 °CTL​ = 5 °CEQH​ = 1200 kJQL​W = ?

A heat engine works between a hot reservoir at 500 °C and a cold reservoir at 5 °C. It takes in 1200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 500 °CTL = 5 °CQH = 1200 kJ
Wmax = kJ
4.Medium
TH​ = 550 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 550 °CTL = 5 °C
ηmax = %
5.Hard
TH​ = 55 °CTL​ = 5 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump delivers 8 kW of heat to a heating system at 55 °C, taking heat from a source at 5 °C. Its actual COP is 40% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 5 °CηII = 40%Q̇H = 8 kW
Ẇ = kW
6.Hard
TH​ = 35 °CTL​ = -10 °CRQ̇H​Q̇L​ = 4.5 kWẆ

A refrigerator keeps its cold space at -10 °C in a kitchen at 35 °C, removing heat from the cold space at 4.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 35 °CTL = -10 °CQ̇L = 4.5 kW
COPmax =

Answer key

  1. 1. Q̇H = 2500 MW
  2. 2. η = 25 %
  3. 3. Wmax = 768.3 kJ
  4. 4. ηmax = 66.21 %
  5. 5. Ẇ = 3.047 kW
  6. 6. COPmax = 5.848

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