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
hot reservoircold reservoirEQH​ = 3400 kJQL​ = 2210 kJW = ?

A heat engine takes in 3400 kJ of heat from a hot reservoir and rejects 2210 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3400 kJQL = 2210 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 30%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 50 MWη = 30%
Q̇L = MW
3.Medium
TH​ = 250 °CTL​ = 40 °CEQH​ = 4000 kJQL​W = ?

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 40 °C. It takes in 4000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 250 °CTL = 40 °CQH = 4000 kJ
Wmax = kJ
4.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 = %
5.Hard
TH​ = 30 °CTL​ = -18 °CRQ̇H​Q̇L​ = 3 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 30 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -18 °CQ̇L = 3 kW
Ẇmin = kW
6.Hard
TH​ = 32 °CTL​ = 5 °CRQ̇H​Q̇L​ = 0.5 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 32 °C, removing heat from the cold space at 0.5 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = 5 °CQ̇L = 0.5 kW
Ẇmin = kW

Answer key

  1. 1. W = 1190 kJ
  2. 2. Q̇L = 116.7 MW
  3. 3. Wmax = 1606 kJ
  4. 4. ηmax = 44.7 %
  5. 5. Ẇmin = 0.5644 kW
  6. 6. Ẇmin = 0.04853 kW

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