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 = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 35%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 35%
Q̇H = MW
2.Easy
houseoutside airHPQ̇H​ = 8 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.4 delivers 8 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.4Q̇H = 8 kW
Q̇L = kW
3.Medium
TH​ = 700 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 700 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 550 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 550 °CTL = 15 °C
ηmax = %
5.Hard
TH​ = 500 °CTL​ = 25 °CEQH​ = 2200 kJQL​ = 1122 kJW = 1078 kJ

A heat engine takes in 2200 kJ of heat from a reservoir at 500 °C, produces 1078 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 500 °CTL = 25 °CQH = 2200 kJW = 1078 kJ
Sgen = kJ/K
6.Hard
TH​ = 500 °CTL​ = 20 °CEQH​ = 4300 kJQL​ = 2967 kJW = 1333 kJ

A heat engine takes in 4300 kJ of heat from a reservoir at 500 °C, produces 1333 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 500 °CTL = 20 °CQH = 4300 kJW = 1333 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇H = 2143 MW
  2. 2. Q̇L = 5.647 kW
  3. 3. ηmax = 70.39 %
  4. 4. ηmax = 64.99 %
  5. 5. Sgen = 0.9177 kJ/K
  6. 6. Sgen = 4.559 kJ/K

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