The sun produces energy at a rate of $3.85 \times 10^{26} \mathrm{W}$ by the fusion of hydrogen. About $0.7 \%$ of each kilogram of hydrogen goes into the energy generated by the Sun. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the sun is $90.0 \%$ hydrogen and half of this can undergo fusion before the sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?
Added by Diane M.
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The energy produced by the fusion of 1 kg of hydrogen is $E = 0.007 \times (3 \times 10^8 \, m/s)^2 = 6.3 \times 10^{13} \, J$. The rate at which the Sun produces energy is $3.85 \times 10^{26} \, W = 3.85 \times 10^{26} \, J/s$. Show more…
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