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
houseoutside airHPQ̇H​ = 14.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4 delivers 14.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4Q̇H = 14.5 kW
Q̇L = kW
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 30%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 750 MWη = 30%
Q̇L = MW
3.Medium
TH​ = 225 °CTL​ = ?EQH​ = 4800 kJQL​ = 2680 kJW

A reversible (Carnot) heat engine takes in 4800 kJ of heat from a reservoir at 225 °C and rejects 2680 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 225 °CQH = 4800 kJQL = 2680 kJ
TL = °C
4.Medium
TH​ = 750 °CTL​ = ?EQH​ = 1100 kJQL​ = 342 kJW

A reversible (Carnot) heat engine takes in 1100 kJ of heat from a reservoir at 750 °C and rejects 342 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 750 °CQH = 1100 kJQL = 342 kJ
TL = °C
5.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 0 °C outside, delivering 15 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 0 °CQ̇H = 15 kW
Ẇmin = kW
6.Hard
TH​ = 400 °CTL​ = 40 °CEQH​ = 4500 kJQL​ = 3060 kJW = 1440 kJ

A heat engine takes in 4500 kJ of heat from a reservoir at 400 °C, produces 1440 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 400 °CTL = 40 °CQH = 4500 kJW = 1440 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇L = 10.88 kW
  2. 2. Q̇L = 1750 MW
  3. 3. TL = 4.984 °C
  4. 4. TL = 44.96 °C
  5. 5. Ẇmin = 1.023 kW
  6. 6. Sgen = 3.087 kJ/K

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