Answer:
Power Output = 42 KW
T₁ = 1152 K = 879°C
Explanation:
The thermal efficiency of a Carnot's Engine is given by:
η = 1 - Q₂/Q₁
where,
η = efficiency = 75% = 0.75
Q₂ = Heat Rejection Rate = 14 KW
Q₁ = Heat Absorption Rate = ?
Therefore,
0.75 = 1 - 14 KW/Q₁
14 KW = (1 - 0.75)(Q₁)
Q₁ = 14 KW/0.25
Q₁ = 56 KW
Thus,
Power Output = Q₁ - Q₂
Power Output = 56 kW - 14 KW
Power Output = 42 KW
The thermal efficiency of a Carnot's Engine is also given by:
η = 1 - T₂/T₁
where,
η = efficiency = 75% = 0.75
T₂ = Temperature of Heat Sink (Lake) = 15°C + 273 = 288 K
T₁ = Temperature of Heat Sink = ?
Therefore,
0.75 = 1 - 288 K/T₁
288 K = (1 - 0.75)(T₁)
T₁ = 288 K/0.25
T₁ = 1152 K = 879°C
