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 = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 45%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 600 MWη = 45%
Q̇L = MW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 1000 MW

A power plant delivers a net power output of 1000 MW with a thermal efficiency of 25%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 1000 MWη = 25%
Q̇H = MW
3.Medium
TH​ = 275 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 275 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 700 °CTL​ = ?EQH​ = 900 kJQL​ = 290 kJW

A reversible (Carnot) heat engine takes in 900 kJ of heat from a reservoir at 700 °C and rejects 290 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 700 °CQH = 900 kJQL = 290 kJ
TL = °C
5.Hard
TH​ = 35 °CTL​ = -20 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 35 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = -20 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 500 °CTL​ = 10 °CEQH​ = 4900 kJQL​ = 2401 kJW = 2499 kJ

A heat engine takes in 4900 kJ of heat from a reservoir at 500 °C, produces 2499 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 500 °CTL = 10 °CQH = 4900 kJW = 2499 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇L = 733.3 MW
  2. 2. Q̇H = 4000 MW
  3. 3. ηmax = 44.7 %
  4. 4. TL = 40.42 °C
  5. 5. Ẇmin = 0.4345 kW
  6. 6. Sgen = 2.142 kJ/K

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