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
hot reservoircold reservoirEQH​ = 1400 kJQL​ = 770 kJW

A heat engine takes in 1400 kJ of heat from a hot reservoir and rejects 770 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1400 kJQL = 770 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 42%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 50 MWη = 42%
Q̇L = MW
3.Medium
TH​ = 475 °CTL​ = ?EQH​ = 1600 kJQL​ = 670 kJW

A reversible (Carnot) heat engine takes in 1600 kJ of heat from a reservoir at 475 °C and rejects 670 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 475 °CQH = 1600 kJQL = 670 kJ
TL = °C
4.Medium
TH​ = 350 °CTL​ = ?EQH​ = 4700 kJQL​ = 2098 kJW

A reversible (Carnot) heat engine takes in 4700 kJ of heat from a reservoir at 350 °C and rejects 2098 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 350 °CQH = 4700 kJQL = 2098 kJ
TL = °C
5.Hard
TH​ = 28 °CTL​ = 5 °CRQ̇H​Q̇L​ = 5 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 28 °C, removing heat from the cold space at 5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = 5 °CQ̇L = 5 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 19.5 kWQ̇L​Ẇ = ?

A heat pump delivers 19.5 kW of heat to a heating system at 22 °C, taking heat from a source at 7 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 7 °CηII = 50%Q̇H = 19.5 kW
Ẇ = kW

Answer key

  1. 1. η = 45 %
  2. 2. Q̇L = 69.05 MW
  3. 3. TL = 40.14 °C
  4. 4. TL = 5.014 °C
  5. 5. Ẇmin = 0.4134 kW
  6. 6. Ẇ = 1.982 kW

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