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
houseoutside airHPQ̇H​ = 8.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.7 delivers 8.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.7Q̇H = 8.5 kW
Ẇ = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 40%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 40%
Q̇H = MW
3.Medium
TH​ = 35 °CTL​ = 2 °CRQ̇H​ = ?Q̇L​ = 8 kWẆ

A reversible refrigerator keeps a cold room at 2 °C by removing 8 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = 2 °CTH = 35 °CQ̇L = 8 kW
Q̇H = kW
4.Medium
TH​ = 250 °CTL​ = 25 °CEQH​ = 4200 kJQL​W = ?

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 25 °C. It takes in 4200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 250 °CTL = 25 °CQH = 4200 kJ
Wmax = kJ
5.Hard
TH​ = 30 °CTL​ = -18 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 30 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -18 °CQ̇L = 1.5 kW
Ẇmin = kW
6.Hard
TH​ = 700 °CTL​ = 20 °CEQH​ = 1300 kJQL​ = 572 kJW = 728 kJ

A heat engine takes in 1300 kJ of heat from a reservoir at 700 °C, produces 728 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 700 °CTL = 20 °CQH = 1300 kJW = 728 kJ
Sgen = kJ/K

Answer key

  1. 1. Ẇ = 3.148 kW
  2. 2. Q̇H = 1875 MW
  3. 3. Q̇H = 8.959 kW
  4. 4. Wmax = 1806 kJ
  5. 5. Ẇmin = 0.2822 kW
  6. 6. Sgen = 0.6154 kJ/K

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