Question

A nuclear power plant operates at 68 % of its maximum theoretical (Carnot) efficiency between temperatures of 665 ∘C and 330 ∘C.

A. If the plant produces electric energy at the rate of 1.4 GW , how much exhaust heat is discharged per hour?

Answer 1

The efficiency of a carnot engine operating between those temperatures is 1 - 330/665 = 50.38%

The power plant is operating at 68% of that, so its efficiency is
50.38 * 0.68 = 34.26 %

So, work / heat energy entering the system = 0.3426
Heat energy entering the system = work / 0.3426
= 1.4 GW / 0.3426
= 4.09 GW

Heat energy entering - work = Heat exhaust
Heat exhaust = 4.09 GW - 1.4 GW
= 2.69 GW
= 2.69 * 10 ^ 9 W = 2.69 * 10 ^ 9 J / s
= 2.69 * 10 ^ 9 J / s * 3600 s / hr
= 747222.3 J / hr