Chapter 31, Problem 23P

To determine

The initial mass to require operating a 650 MW reactor for 1 year.

Answer to Problem 23P

The initial mass to require operating a 650 MW reactor for 1 year is $626.1\text{ kg}$ .

Explanation of Solution

Given:

The efficiency is 40%.

The time of operation is 1 year which is $3.16\times {10}^7\text{ s}$ .

Formula used:

The expression for the actual energy released during fission is given by,

  $\mathrm{Q}=\frac{100}{\mathrm{e}}\mathrm{P}\mathrm{t}$

Calculation:

Substitute the values in the above equation.

  $\begin{array}{c}\mathrm{Q}=\frac{100}{\mathrm{e}}\mathrm{P}\mathrm{t}\\ =\frac{100}{40}\left(650\times {10}^6\right)\left(3.16\times {10}^7\right)\text{ J}\\ =5.135\times {10}^{16}\text{ J}\\ =3.209375\times {10}^{29}\text{MeV}\end{array}$

Calculate the mass of uranium.

  $\begin{array}{c}\mathrm{m}=\frac{\mathrm{Q}}{200}\frac{235\times {10}^{-3}}{{\mathrm{N}}_{\mathrm{A}}}\\ =\left(\frac{3.209\times {10}^{29}}{200}\right)\left(\frac{235\times {10}^{-3}}{6.023\times {10}^{23}}\right)\text{ kg}\\ =626.1\text{ kg}\end{array}$

Thus, the initial mass to require operating a 650 MW reactor for 1 year is $626.1\text{ kg}$ .