Question

What is the power output of ${}_{92}{U}^{235}$ reactor if it takes 30days to use up 2kg of fuel and if each fission gives 185MeV of usable energy? Avogadro's number$=6.02\times {10}^{26}$ per Kmole.

• A. 45 megawatt
• B. 58.46 megawatt
• C. 72 megawatt
• D. 92 megawatt

Answer 1

Answer: (B)

58.46 megawatt

Energy released per fission $=185MeV=185\times 1.6\times {10}^{-13}J$
Fuel Consumption rate $=2kg/30days=\frac{2\times 1000g}{30\times 24\times 3600s}=7.7\times {10}^{-4}g/s$
Rate of decay $=\frac{dN}{dt}=\frac{7.7\times {10}^{-4}\times \left(N_A\right)}{235}=1.96\times {10}^{18}/s$
Power generated $=\frac{dN}{dt}E=1.96\times {10}^{18}\times 185MeV$
$=58.4MW$