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​ = 5.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.9 delivers 5.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.9Q̇H = 5.5 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 3600 kJQL​ = 2700 kJW

A heat engine takes in 3600 kJ of heat from a hot reservoir and rejects 2700 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3600 kJQL = 2700 kJ
η = %
3.Medium
TH​ = 650 °CTL​ = 30 °CEQH​ = 3400 kJQL​W = ?

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 30 °C. It takes in 3400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 650 °CTL = 30 °CQH = 3400 kJ
Wmax = kJ
4.Medium
TH​ = 350 °CTL​ = ?EQH​ = 2900 kJQL​ = 1271 kJW

A reversible (Carnot) heat engine takes in 2900 kJ of heat from a reservoir at 350 °C and rejects 1271 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 350 °CQH = 2900 kJQL = 1271 kJ
TL = °C
5.Hard
TH​ = 32 °CTL​ = -18 °CRQ̇H​Q̇L​ = 3.5 kWẆ

A refrigerator keeps its cold space at -18 °C in a kitchen at 32 °C, removing heat from the cold space at 3.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = -18 °CQ̇L = 3.5 kW
COPmax =
6.Hard
850 °CTm​ = ?10 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 850 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 10 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 850 °CTL = 10 °C
Tm = °C

Answer key

  1. 1. Ẇ = 1.41 kW
  2. 2. η = 25 %
  3. 3. Wmax = 2283 kJ
  4. 4. TL = −0.0384 °C
  5. 5. COPmax = 5.103
  6. 6. Tm = 290.8 °C

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