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
hot reservoircold reservoirEQH​ = 1800 kJQL​ = 1350 kJW

A heat engine takes in 1800 kJ of heat from a hot reservoir and rejects 1350 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1800 kJQL = 1350 kJ
η = %
3.Medium
TH​ = 20 °CTL​ = 2 °CRQ̇H​ = ?Q̇L​ = 0.5 kWẆ

A reversible refrigerator keeps a cold room at 2 °C by removing 0.5 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = 2 °CTH = 20 °CQ̇L = 0.5 kW
Q̇H = kW
4.Medium
TH​ = 600 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 600 °CTL = 15 °C
ηmax = %
5.Hard
TH​ = 600 °CTL​ = 30 °CEQH​ = 4300 kJQL​ = 2881 kJW = 1419 kJ

A heat engine takes in 4300 kJ of heat from a reservoir at 600 °C, produces 1419 kJ of work and rejects the rest to a reservoir at 30 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 600 °CTL = 30 °CQH = 4300 kJW = 1419 kJ
Sgen = kJ/K
6.Hard
TH​ = 30 °CTL​ = -25 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 30 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -25 °CQ̇L = 4 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 2143 MW
  2. 2. η = 25 %
  3. 3. Q̇H = 0.5327 kW
  4. 4. ηmax = 67 %
  5. 5. Sgen = 4.579 kJ/K
  6. 6. Ẇmin = 0.8866 kW

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