Chapter 31, Problem 31P

To determine

To find:The mass of deuterium fuel

Answer to Problem 31P

  $0.388\text{g}$

Explanation of Solution

Given data:

The reaction of Eq. $31-8\text{b}$ consumes 2 deuterons and releases $3.23\text{MeV}$ of energy

If 2 deuterium released 3.23 MeV and one mole of deuterium is equal to $2.014\times {10}^{-3}\text{kg}$

The mass of deuterium require to generate 950 W power is

  $\begin{array}{l}\left(950\frac{\text{J}}{\text{s}}\right)(1\text{yr})\left(3.156\times {10}^7\frac{\text{s}}{\text{yr}}\right)\left(\frac{1\text{MeV}}{1.60\times {10}^{-13}\text{J}}\right)\left(\frac{2\text{d}}{3.23\text{MeV}}\right)\left(\frac{2.014\times {10}^{-3}\text{kg}}{6.02\times {10}^{23}\text{d}}\right)\hfill \\ \begin{array}{l}=3.88\times {10}^{-4}\text{kg}\\ =0.388\text{g}\end{array}\hfill \end{array}$

Conclusion:

  $0.388\text{g}$