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 = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 25%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 3800 kJQL​ = 2280 kJW = ?

A heat engine takes in 3800 kJ of heat from a hot reservoir and rejects 2280 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3800 kJQL = 2280 kJ
W = kJ
3.Medium
TH​ = 525 °CTL​ = 35 °CEQH​ = 700 kJQL​W = ?

A heat engine works between a hot reservoir at 525 °C and a cold reservoir at 35 °C. It takes in 700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 525 °CTL = 35 °CQH = 700 kJ
Wmax = kJ
4.Medium
TH​ = 375 °CTL​ = ?EQH​ = 1600 kJQL​ = 724 kJW

A reversible (Carnot) heat engine takes in 1600 kJ of heat from a reservoir at 375 °C and rejects 724 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 375 °CQH = 1600 kJQL = 724 kJ
TL = °C
5.Hard
TH​ = 750 °CT0​ = 20 °CTL​ = -30 °CERWQ̇H​ = 20 kWQ̇L​ = ?

A Carnot heat engine receives 20 kW of heat from a source at 750 °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 -30 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 750 °CT0 = 20 °CTL = -30 °CQ̇H = 20 kW
Q̇L = kW
6.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 11.5 kWQ̇L​Ẇ = ?

A heat pump delivers 11.5 kW of heat to a heating system at 22 °C, taking heat from a source at 2 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 2 °CηII = 45%Q̇H = 11.5 kW
Ẇ = kW

Answer key

  1. 1. Q̇L = 600 MW
  2. 2. W = 1520 kJ
  3. 3. Wmax = 429.7 kJ
  4. 4. TL = 20.14 °C
  5. 5. Q̇L = 69.39 kW
  6. 6. Ẇ = 1.732 kW

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