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​ = 0.72 kWẆ = 0.3 kW

A refrigerator removes heat from its cold space at a rate of 0.72 kW while its compressor uses 0.3 kW of power. Find its coefficient of performance COPR.

Q̇L = 0.72 kWẆ = 0.3 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 500 MW

A power plant delivers a net power output of 500 MW with a thermal efficiency of 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 500 MWη = 25%
Q̇L = MW
3.Medium
TH​ = 725 °CTL​ = ?EQH​ = 3600 kJQL​ = 1057 kJW

A reversible (Carnot) heat engine takes in 3600 kJ of heat from a reservoir at 725 °C and rejects 1057 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 725 °CQH = 3600 kJQL = 1057 kJ
TL = °C
4.Medium
TH​ = 525 °CTL​ = 35 °CEQH​ = 2700 kJQL​W = ?

A heat engine works between a hot reservoir at 525 °C and a cold reservoir at 35 °C. It takes in 2700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 525 °CTL = 35 °CQH = 2700 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = 0 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump delivers 5 kW of heat to a heating system at 22 °C, taking heat from a source at 0 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 0 °CηII = 30%Q̇H = 5 kW
Ẇ = kW
6.Hard
TH​ = 28 °CTL​ = -20 °CRQ̇H​Q̇L​ = 2.5 kWẆ

A refrigerator keeps its cold space at -20 °C in a kitchen at 28 °C, removing heat from the cold space at 2.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = -20 °CQ̇L = 2.5 kW
COPmax =

Answer key

  1. 1. COPR = 2.4
  2. 2. Q̇L = 1500 MW
  3. 3. TL = 19.92 °C
  4. 4. Wmax = 1658 kJ
  5. 5. Ẇ = 1.242 kW
  6. 6. COPmax = 5.274

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