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​ = 1800 kJQL​ = 990 kJW = ?

A heat engine takes in 1800 kJ of heat from a hot reservoir and rejects 990 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1800 kJQL = 990 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 150 MW

A power plant delivers a net power output of 150 MW with a thermal efficiency of 42%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 150 MWη = 42%
Q̇L = MW
3.Medium
TH​ = 600 °CTL​ = ?EQH​ = 3100 kJQL​ = 1005 kJW

A reversible (Carnot) heat engine takes in 3100 kJ of heat from a reservoir at 600 °C and rejects 1005 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 600 °CQH = 3100 kJQL = 1005 kJ
TL = °C
4.Medium
TH​ = 775 °CTL​ = ?EQH​ = 800 kJQL​ = 239 kJW

A reversible (Carnot) heat engine takes in 800 kJ of heat from a reservoir at 775 °C and rejects 239 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 775 °CQH = 800 kJQL = 239 kJ
TL = °C
5.Hard
TH​ = 21 °CTL​ = 5 °CHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump delivers 11 kW of heat to a heating system at 21 °C, taking heat from a source at 5 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = 5 °CηII = 35%Q̇H = 11 kW
Ẇ = kW
6.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 15 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is -5 °C outside, delivering 15 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = -5 °CQ̇H = 15 kW
COPmax =

Answer key

  1. 1. W = 810 kJ
  2. 2. Q̇L = 207.1 MW
  3. 3. TL = 9.92 °C
  4. 4. TL = 39.98 °C
  5. 5. Ẇ = 1.71 kW
  6. 6. COPmax = 11.31

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