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 = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 30%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 30%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 1600 kJQL​ = 1040 kJW = ?

A heat engine takes in 1600 kJ of heat from a hot reservoir and rejects 1040 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1600 kJQL = 1040 kJ
W = kJ
3.Medium
TH​ = 775 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 775 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 775 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 28 °CTL​ = -20 °CRQ̇H​ = ?Q̇L​ = 4.5 kWẆ

A reversible refrigerator keeps a cold room at -20 °C by removing 4.5 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = -20 °CTH = 28 °CQ̇L = 4.5 kW
Q̇H = kW
5.Hard
TH​ = 800 °CTL​ = 20 °CEQH​ = 800 kJQL​ = 392 kJW = 408 kJ

A heat engine takes in 800 kJ of heat from a reservoir at 800 °C, produces 408 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 800 °CTL = 20 °CQH = 800 kJW = 408 kJ
Sgen = kJ/K
6.Hard
TH​ = 800 °CTL​ = 40 °CEQH​ = 3600 kJQL​ = 1548 kJW = 2052 kJ

A heat engine takes in 3600 kJ of heat from a reservoir at 800 °C, produces 2052 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 = 3600 kJW = 2052 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇L = 466.7 MW
  2. 2. W = 560 kJ
  3. 3. ηmax = 70.6 %
  4. 4. Q̇H = 5.353 kW
  5. 5. Sgen = 0.5917 kJ/K
  6. 6. Sgen = 1.589 kJ/K

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