Question

A nuclear power plant generates a total of 3 GW of power at an efficiency of 33%. The nuclear reactor has a recoverable energy per fission of 210 MeV. Approximately 65% of the plant's power comes from fissions in 235U, the remainder from fissions in plutonium, 239Pu. calculate: (a) the net electric power output, (b) the rate of fission events (per second) in the reactor core, (c) the mass of 235U used up in one year (hint: every fission event consumes one 235U nucleus and in the reactor core about 1.0 (1020) nuclei of U 235 are consumed every second. (d) If the plant were operated at full power for 1 year, how many

Answer 1

Answer:

Explanation:

From the question we are told that:

Plant Generates $P=3GW$

Efficiency $\eta =33\%$

Recoverable energy per fission $\mu=210MeV \approx 336.42*18^{-7}J$

Fission Power $F_p=235U$ $(65\% of Plant\ power)$

Fission in plutonium $F_{pl}=239Pu$

a)

Generally the equation for net electric power output $P_o$ is mathematically given by

$P_o=P*\frac{1}{\eta}$

$P_o=3*\frac{100}{3}$

$P_o=9.0GW$

b)

Generally the equation for Rate of Fission $F_{rate}$ is mathematically given by

$F_{rate}=\frac{P_o}{\mu}}$

$F_{rate}=\frac{9*10^{9}}{336.42*18^{-7}}}$

$F_{rate}=27.02*10^{13}$

c)

Generally the equation for  Mass of $^{235} U$ used in a yr $M_{U/yr}$ is mathematically given by

$M_{U/yr}=P_o*\frac{65}{100}$

$M_{U/yr}=5.91GW$