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 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 100 MWη = 30%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 1300 kJQL​ = 780 kJW = ?

A heat engine takes in 1300 kJ of heat from a hot reservoir and rejects 780 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1300 kJQL = 780 kJ
W = kJ
3.Medium
TH​ = 250 °CTL​ = ?EQH​ = 3500 kJQL​ = 1995 kJW

A reversible (Carnot) heat engine takes in 3500 kJ of heat from a reservoir at 250 °C and rejects 1995 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 250 °CQH = 3500 kJQL = 1995 kJ
TL = °C
4.Medium
TH​ = 700 °CTL​ = ?EQH​ = 2000 kJQL​ = 602 kJW

A reversible (Carnot) heat engine takes in 2000 kJ of heat from a reservoir at 700 °C and rejects 602 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 700 °CQH = 2000 kJQL = 602 kJ
TL = °C
5.Hard
TH​ = 850 °CT0​ = 30 °CTL​ = -15 °CERWQ̇H​ = 30 kWQ̇L​ = ?

A Carnot heat engine receives 30 kW of heat from a source at 850 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 850 °CT0 = 30 °CTL = -15 °CQ̇H = 30 kW
Q̇L = kW
6.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -10 °CQ̇H = 5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 333.3 MW
  2. 2. W = 520 kJ
  3. 3. TL = 25.05 °C
  4. 4. TL = 19.77 °C
  5. 5. Q̇L = 125.6 kW
  6. 6. Ẇmin = 0.5421 kW

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