Physics

Problem

Coal releases about

3.0\times10^{7}\,\mathrm{J\,kg^{-1}}

when burnt, whereas the fission of

^{235}\!\mathrm{U}

releases approximately

200\,\mathrm{MeV}

per nucleus. a. (i) Derive an expression for the ratio

\dfrac{m_{\text{coal}}}{m_{\text{U}}}

of the masses of coal and

^{235}\!\mathrm{U}

that would yield the same total energy output, starting from the given microscopic and macroscopic data. b. (ii) Using

1\,\mathrm{eV}=1.602\times10^{-19}\,\mathrm{J}

and Avogadro number

6.022\times10^{23}\,\mathrm{mol^{-1}}

, calculate numerically the mass of coal required to produce the same energy as

1.0\,\mathrm{kg}

^{235}\!\mathrm{U}

fissioned completely. c. (iii) Comment on two logistic or environmental advantages that the result in part (ii) confers on nuclear power stations over conventional coal-based stations.

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