Question

A nuclear power plant operates at 68 % of its maximum theoretical (Carnot) efficiency between temperatures of 680 ∘C and 400 ∘C. Part A If the plant produces electric energy at the rate of 1.5 GW , how much exhaust heat is discharged per hour? Express your answer using two significant figures.

Answer 1

Answer:

13860 Giga Joule/hour

Explanation:

$T_h=\text{temperature of high temperature reservoir}=680^ {\circ}C\\T_l=\text{temperature of low temperature reservoir}=400^ {\circ}C\\W=Work\ done=1.5\ GW\\Q_l=\text{low temperature reservoir heat = exhaust heat discharged}\\Q_h=\text{high temperature reservoir heat}\\\eta=\text{Carnot efficiency}\\\eta_{actual}=0.68\eta$

$\eta=1-\frac{T_c}{T_h}\\\Rightarrow \eta=1-\frac{400}{680}\\\Rightarrow \eta=1-0.58\\\Rightarrow \eta=0.41$

$\eta_{actual}=0.68\eta\\\Rightarrow \eta_{actual}=0.68\times0.41\\\Rightarrow\eta_{actual}=0.28$

$\eta_{actual}=\frac{W}{Q_h}\\\Rightarrow Q_h=\frac{W}{\eta_{actual}}\\\Rightarrow Q_h=\frac{1.5}{0.28}\\\Rightarrow Q_h=5.35\ GW$

$Q_l=Q_h-W\\\Rightarrow Q_l=5.35-1.5\\\Rightarrow Q_l=3.85\ GW$

$3.85\ GW=3.85\ GJ/s\\1\ GW=3600\ GJ/h\\\Rightarrow 3.85\ GW=13860\ GJoule/hour$

∴ Exhaust heat discharged is 13860 Giga Joule/hour