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
kitchencold spaceRQ̇H​ = ?Q̇L​ = 0.84 kWẆ = 0.4 kW

A refrigerator removes heat from its cold space at a rate of 0.84 kW while its compressor uses 0.4 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 0.84 kWẆ = 0.4 kW
Q̇H = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 42%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 600 MWη = 42%
Q̇H = MW
3.Medium
TH​ = 25 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 5.5 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 5.5 kW of heat, and rejects heat to the surroundings at 25 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 25 °CQ̇L = 5.5 kW
Q̇H = kW
4.Medium
TH​ = 425 °CTL​ = ?EQH​ = 5000 kJQL​ = 2028 kJW

A reversible (Carnot) heat engine takes in 5000 kJ of heat from a reservoir at 425 °C and rejects 2028 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 425 °CQH = 5000 kJQL = 2028 kJ
TL = °C
5.Hard
TH​ = 45 °CTL​ = -5 °CHPQ̇H​ = 19.5 kWQ̇L​Ẇ = ?

A heat pump delivers 19.5 kW of heat to a heating system at 45 °C, taking heat from a source at -5 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = -5 °CηII = 45%Q̇H = 19.5 kW
Ẇ = kW
6.Hard
TH​ = 32 °CTL​ = -10 °CRQ̇H​Q̇L​ = 3.5 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 32 °C, removing heat from the cold space at 3.5 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -10 °CQ̇L = 3.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 1.24 kW
  2. 2. Q̇H = 1429 MW
  3. 3. Q̇H = 6.427 kW
  4. 4. TL = 10.02 °C
  5. 5. Ẇ = 6.81 kW
  6. 6. Ẇmin = 0.5586 kW

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