The Nuclear Reactor — Question 1

Question 1

A nuclear power station balances electrical output and rejected heat

A station delivers 900 MW of electrical power at thermal efficiency .360. Treat all other thermal energy as rejected to the environment.

1. Calculate thermal input power and waste heat rate.

2. At the same electrical output, an improved efficiency of .400 is proposed. Find the reduction in thermal input and waste heat.

Question 1 - Solution

A nuclear power station balances electrical output and rejected heat

(a) Method and calculation

$$\eta=P_e/P_{\mathrm{th}}\Rightarrow\boxed{P_{\mathrm{th}}=900/.360=2500\,\mathrm{MW}}.$$$$\boxed{P_{\mathrm{waste}}=P_{\mathrm{th}}-P_e=1600\,\mathrm{MW}}.$$

(b) Interpretation and further calculation

$$\boxed{P_{\mathrm{th}}\prime=900/.400=2250\,\mathrm{MW},\quad P_{\mathrm{waste}}\prime=1350\,\mathrm{MW}}.$$$$\boxed{\Delta P_{\mathrm{th}}=\Delta P_{\mathrm{waste}}=-250\,\mathrm{MW}}.$$

Physical check

Greater conversion efficiency reduces rejected heat at fixed electrical output. Thermal power and electrical power must not be interchanged.