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Additional Exercises · 13.31

Q.Suppose India had a target of producing by 2020 AD, 200,000 MW of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was 25%. How much amount of fissionable uranium would our country need per year by 2020? Take the heat energy per fission of 235U^{235}\text{U} to be about 200MeV.

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Find the required nuclear electric output (10% of 200,000 MW), convert to thermal power using the 25% efficiency, find the annual thermal energy, divide by 200 MeV/fission to get the number of fissions, and convert to mass. Result: about 3.08 × 10⁴ kg (roughly 30.8 tonnes) of U-235 per year.

Step 1 — Required nuclear electric power

Pelec=10%×200,000 MW=20,000 MW=2×1010 WP_{\text{elec}} = 10\% \times 200{,}000\ \text{MW} = 20{,}000\ \text{MW} = 2\times10^{10}\ \text{W}

Step 2 — Required thermal power

Since only 25% of thermal energy converts to electricity:

Pthermal=Pelec0.25=2×10100.25=8×1010 WP_{\text{thermal}} = \frac{P_{\text{elec}}}{0.25} = \frac{2\times10^{10}}{0.25} = 8\times10^{10}\ \text{W}

Step 3 — Thermal energy needed per year

Eyear=Pthermal×(1 yr in seconds)=8×1010×3.154×107=2.5232×1018 JE_{\text{year}} = P_{\text{thermal}} \times (1\ \text{yr in seconds}) = 8\times10^{10} \times 3.154\times10^{7} = 2.5232\times10^{18}\ \text{J}

Step 4 — Number of fissions needed

Efission=200 MeV=200×1.6×10−13=3.2×10−11 JE_{\text{fission}} = 200\ \text{MeV} = 200\times1.6\times10^{-13} = 3.2\times10^{-11}\ \text{J}

N=2.5232×10183.2×10−11=7.885×1028 fissions/yearN = \frac{2.5232\times10^{18}}{3.2\times10^{-11}} = 7.885\times10^{28}\ \text{fissions/year}

Step 5 — Mass of U-235 needed …

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