If a power plant produces steam at 600 $\circ$ C and outputs heat at 150 $\circ$ C to a cogeneration power plant that then outputs its exhaust at a temperature of 40 $\circ$ C.Find the total efficiency of this combination of power plants.Assume both plants are 80% as efficient as a Carnot heat engine.

Question

Quizplus · Accepted Answer

The efficiency of a Carnot heat engine can be calculated as:
Efficiency = 1 - (T_cold/T_hot)
where T_cold and T_hot are the temperatures of the cold and hot reservoirs, respectively. 
For a Carnot engine operating between 600F and 150F, the efficiency is:
Efficiency1 = 1 - (423.15K/811.15K) = 0.478 = 47.8%
For a Carnot engine operating between 150F and 40F, the efficiency is:
Efficiency2 = 1 - (277.15K/422.15K) = 0.34 = 34%
Assuming both plants are 80% as efficient as a Carnot engine, the overall efficiency can be calculated as:
Overall efficiency = Efficiency1 x Efficiency2 x 0.8^2 = 0.478 x 0.34 x 0.64 = 0.053 = 5.3%
Therefore, the best choice is D, 53%.

If a Power Plant Produces Steam at 600 ∘\circ∘ C and Outputs Heat at 150

If a Power Plant Produces Steam at 600^$\circ$C and Outputs Heat at 150