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​ = 2.1 kWẆ = 1.4 kW

A refrigerator removes heat from its cold space at a rate of 2.1 kW while its compressor uses 1.4 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.1 kWẆ = 1.4 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 1000 kJQL​ = 550 kJW = ?

A heat engine takes in 1000 kJ of heat from a hot reservoir and rejects 550 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1000 kJQL = 550 kJ
W = kJ
3.Medium
TH​ = 20 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 7.5 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 7.5 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 20 °CQ̇L = 7.5 kW
Q̇H = kW
4.Medium
TH​ = 525 °CTL​ = ?EQH​ = 500 kJQL​ = 202 kJW

A reversible (Carnot) heat engine takes in 500 kJ of heat from a reservoir at 525 °C and rejects 202 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 525 °CQH = 500 kJQL = 202 kJ
TL = °C
5.Hard
TH​ = 850 °CTL​ = 40 °CEQH​ = 4200 kJQL​ = 2688 kJW = 1512 kJ

A heat engine takes in 4200 kJ of heat from a reservoir at 850 °C, produces 1512 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 850 °CTL = 40 °CQH = 4200 kJW = 1512 kJ
Sgen = kJ/K
6.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 15 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is 7 °C outside, delivering 15 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = 7 °CQ̇H = 15 kW
COPmax =

Answer key

  1. 1. Q̇H = 3.5 kW
  2. 2. W = 450 kJ
  3. 3. Q̇H = 8.617 kW
  4. 4. TL = 49.3 °C
  5. 5. Sgen = 4.844 kJ/K
  6. 6. COPmax = 22.55

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