A nuclear power plant operates at 70 of its maximum theoreti

A nuclear power plant operates at 70% of its maximum theoretical (Carnot) efficiency between temperatures of 670° and 320°C. If the plant produces electric energy at the rate of 1.3 GW, how much exhaust heat is discharged per hour?

Solution

The Carnot efficiency = 1 - (T_c / T_h)

= 1 - [ (320 + 273) / (670 + 273) ] = 0.3711

A nuclear power plant operates at 70%

real efficiency = 0.3711 * (70 / 100) = 0.2598

The efficiency is equal to the ratio of energy extracted to the energy input

0.2598 = (1.3 GW) / (1.3 GW + exhaust)

1.3 GW + exhaust = 5.00

exhaust = 3.70 GW = 3.70 GJ/s = 3.70 * 10⁹ J/s

= 1.33 * 10¹³ J/hr