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​ = 3800 kJQL​ = 2850 kJW = ?

A heat engine takes in 3800 kJ of heat from a hot reservoir and rejects 2850 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3800 kJQL = 2850 kJ
W = kJ
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 3.45 kWẆ = 1.5 kW

A refrigerator removes heat from its cold space at a rate of 3.45 kW while its compressor uses 1.5 kW of power. Find its coefficient of performance COPR.

Q̇L = 3.45 kWẆ = 1.5 kW
COPR =
3.Medium
TH​ = 575 °CTL​ = ?EQH​ = 1800 kJQL​ = 612 kJW

A reversible (Carnot) heat engine takes in 1800 kJ of heat from a reservoir at 575 °C and rejects 612 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 575 °CQH = 1800 kJQL = 612 kJ
TL = °C
4.Medium
TH​ = 30 °CTL​ = -25 °CRQ̇H​ = ?Q̇L​ = 1 kWẆ

A reversible refrigerator keeps a cold room at -25 °C by removing 1 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = -25 °CTH = 30 °CQ̇L = 1 kW
Q̇H = kW
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 11 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 11 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 7 °CQ̇H = 11 kW
COPmax =
6.Hard
TH​ = 800 °CTL​ = 40 °CEQH​ = 3000 kJQL​ = 1740 kJW = 1260 kJ

A heat engine takes in 3000 kJ of heat from a reservoir at 800 °C, produces 1260 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 800 °CTL = 40 °CQH = 3000 kJW = 1260 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 950 kJ
  2. 2. COPR = 2.3
  3. 3. TL = 15.22 °C
  4. 4. Q̇H = 1.222 kW
  5. 5. COPmax = 19.68
  6. 6. Sgen = 2.761 kJ/K

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