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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Name: ____________________   Date: ____________

1.Easy
houseoutside airHPQ̇H​ = 18.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.4 delivers 18.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.4Q̇H = 18.5 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.4 delivers 10 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.4Q̇H = 10 kW
Ẇ = kW
3.Medium
TH​ = 625 °CTL​ = ?EQH​ = 4600 kJQL​ = 1501 kJW

A reversible (Carnot) heat engine takes in 4600 kJ of heat from a reservoir at 625 °C and rejects 1501 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 625 °CQH = 4600 kJQL = 1501 kJ
TL = °C
4.Medium
TH​ = 350 °CTL​ = ?EQH​ = 2700 kJQL​ = 1292 kJW

A reversible (Carnot) heat engine takes in 2700 kJ of heat from a reservoir at 350 °C and rejects 1292 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 350 °CQH = 2700 kJQL = 1292 kJ
TL = °C
5.Hard
TH​ = 500 °CTL​ = 35 °CEQH​ = 2100 kJQL​ = 1470 kJW = 630 kJ

A heat engine takes in 2100 kJ of heat from a reservoir at 500 °C, produces 630 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 500 °CTL = 35 °CQH = 2100 kJW = 630 kJ
Sgen = kJ/K
6.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 11 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 5 °CQ̇H = 11 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 4.205 kW
  2. 2. Ẇ = 2.941 kW
  3. 3. TL = 19.92 °C
  4. 4. TL = 25.04 °C
  5. 5. Sgen = 2.054 kJ/K
  6. 6. Ẇmin = 0.6336 kW

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