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 = 100 MW

A power plant delivers a net power output of 100 MW with a thermal efficiency of 42%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 100 MWη = 42%
Q̇L = MW
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 2.16 kWẆ = 1.2 kW

A refrigerator removes heat from its cold space at a rate of 2.16 kW while its compressor uses 1.2 kW of power. Find its coefficient of performance COPR.

Q̇L = 2.16 kWẆ = 1.2 kW
COPR =
3.Medium
TH​ = 200 °CTL​ = 25 °CEQH​ = 1300 kJQL​W = ?

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 25 °C. It takes in 1300 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 200 °CTL = 25 °CQH = 1300 kJ
Wmax = kJ
4.Medium
TH​ = 800 °CTL​ = ?EQH​ = 2100 kJQL​ = 564 kJW

A reversible (Carnot) heat engine takes in 2100 kJ of heat from a reservoir at 800 °C and rejects 564 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 800 °CQH = 2100 kJQL = 564 kJ
TL = °C
5.Hard
TH​ = 35 °CTL​ = -10 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at -10 °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 = -10 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 900 °CTL​ = 10 °CEQH​ = 800 kJQL​ = 496 kJW = 304 kJ

A heat engine takes in 800 kJ of heat from a reservoir at 900 °C, produces 304 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 900 °CTL = 10 °CQH = 800 kJW = 304 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇L = 138.1 MW
  2. 2. COPR = 1.8
  3. 3. Wmax = 480.8 kJ
  4. 4. TL = 15.07 °C
  5. 5. Ẇmin = 0.342 kW
  6. 6. Sgen = 1.07 kJ/K

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