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 = 1000 MW

A power plant delivers a net power output of 1000 MW with a thermal efficiency of 55%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 1000 MWη = 55%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 2300 kJQL​ = 1725 kJW = ?

A heat engine takes in 2300 kJ of heat from a hot reservoir and rejects 1725 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2300 kJQL = 1725 kJ
W = kJ
3.Medium
TH​ = 800 °CTL​ = ?EQH​ = 4700 kJQL​ = 1196 kJW

A reversible (Carnot) heat engine takes in 4700 kJ of heat from a reservoir at 800 °C and rejects 1196 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 800 °CQH = 4700 kJQL = 1196 kJ
TL = °C
4.Medium
TH​ = 600 °CTL​ = 5 °CEQH​ = 4700 kJQL​W = ?

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 5 °C. It takes in 4700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 600 °CTL = 5 °CQH = 4700 kJ
Wmax = kJ
5.Hard
TH​ = 20 °CTL​ = 5 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 5 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 5 °CQ̇H = 5 kW
Ẇmin = kW
6.Hard
900 °CTm​ = ?35 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 900 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 35 °C. Both engines produce the same work. Find Tm in °C.

TH = 900 °CTL = 35 °C
Tm = °C

Answer key

  1. 1. Q̇L = 818.2 MW
  2. 2. W = 575 kJ
  3. 3. TL = −0.06757 °C
  4. 4. Wmax = 3203 kJ
  5. 5. Ẇmin = 0.2558 kW
  6. 6. Tm = 467.5 °C

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