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 = 500 MW

A power plant delivers a net power output of 500 MW with a thermal efficiency of 35%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 500 MWη = 35%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 2300 kJQL​ = 1495 kJW

A heat engine takes in 2300 kJ of heat from a hot reservoir and rejects 1495 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2300 kJQL = 1495 kJ
η = %
3.Medium
TH​ = 250 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 250 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 650 °CTL​ = ?EQH​ = 1700 kJQL​ = 577 kJW

A reversible (Carnot) heat engine takes in 1700 kJ of heat from a reservoir at 650 °C and rejects 577 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 650 °CQH = 1700 kJQL = 577 kJ
TL = °C
5.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -10 °CQ̇H = 14 kW
Ẇmin = kW
6.Hard
TH​ = 30 °CTL​ = -20 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 30 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -20 °CQ̇L = 1.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 928.6 MW
  2. 2. η = 35 %
  3. 3. ηmax = 46.83 %
  4. 4. TL = 40.18 °C
  5. 5. Ẇmin = 1.475 kW
  6. 6. Ẇmin = 0.2963 kW

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