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 55%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 100 MWη = 55%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 2400 kJQL​ = 1440 kJW

A heat engine takes in 2400 kJ of heat from a hot reservoir and rejects 1440 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2400 kJQL = 1440 kJ
η = %
3.Medium
TH​ = 40 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 6.5 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 6.5 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 40 °CQ̇L = 6.5 kW
Q̇H = kW
4.Medium
TH​ = 675 °CTL​ = ?EQH​ = 1800 kJQL​ = 557 kJW

A reversible (Carnot) heat engine takes in 1800 kJ of heat from a reservoir at 675 °C and rejects 557 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 675 °CQH = 1800 kJQL = 557 kJ
TL = °C
5.Hard
TH​ = 25 °CTL​ = 4 °CRQ̇H​Q̇L​ = 2.5 kWẆ

A refrigerator keeps its cold space at 4 °C in a kitchen at 25 °C, removing heat from the cold space at 2.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 25 °CTL = 4 °CQ̇L = 2.5 kW
COPmax =
6.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 15 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 15 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 7 °CQ̇H = 15 kW
COPmax =

Answer key

  1. 1. Q̇H = 181.8 MW
  2. 2. η = 40 %
  3. 3. Q̇H = 7.978 kW
  4. 4. TL = 20.25 °C
  5. 5. COPmax = 13.2
  6. 6. COPmax = 19.68

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