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 55%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 750 MWη = 55%
Q̇L = MW
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 8.61 kWẆ = 2.1 kW

A refrigerator removes heat from its cold space at a rate of 8.61 kW while its compressor uses 2.1 kW of power. Find its coefficient of performance COPR.

Q̇L = 8.61 kWẆ = 2.1 kW
COPR =
3.Medium
TH​ = 200 °CTL​ = 25 °CEQH​ = 1400 kJQL​W = ?

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 25 °C. It takes in 1400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 200 °CTL = 25 °CQH = 1400 kJ
Wmax = kJ
4.Medium
TH​ = 500 °CTL​ = ?EQH​ = 3300 kJQL​ = 1379 kJW

A reversible (Carnot) heat engine takes in 3300 kJ of heat from a reservoir at 500 °C and rejects 1379 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 500 °CQH = 3300 kJQL = 1379 kJ
TL = °C
5.Hard
TH​ = 650 °CT0​ = 25 °CTL​ = -25 °CERWQ̇H​ = 200 kWQ̇L​ = ?

A Carnot heat engine receives 200 kW of heat from a source at 650 °C and rejects heat to the surroundings at 25 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -25 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 25 °CTL = -25 °CQ̇H = 200 kW
Q̇L = kW
6.Hard
TH​ = 900 °CT0​ = 20 °CTL​ = -25 °CERWQ̇H​ = 110 kWQ̇L​ = ?

A Carnot heat engine receives 110 kW of heat from a source at 900 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -25 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 900 °CT0 = 20 °CTL = -25 °CQ̇H = 110 kW
Q̇L = kW

Answer key

  1. 1. Q̇L = 613.6 MW
  2. 2. COPR = 4.1
  3. 3. Wmax = 517.8 kJ
  4. 4. TL = 49.93 °C
  5. 5. Q̇L = 672 kW
  6. 6. Q̇L = 455 kW

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