A 1.0\,GW electric power station is to be operated continuously for exactly one calendar year.
Consider two possible fuels:
• High-grade coal with an energy content of 3.0×107Jkg−1 (assume the conversion from heat to electricity is 40% efficient).
• Enriched uranium-235, which releases 200MeV per fission (assume the conversion from nuclear heat to electricity is 32% efficient).
Neglect any other losses.
(i) Compute the total electrical energy the station must deliver in one year.
(ii) Calculate the total thermal energy that must be generated when the station is fired by coal and hence obtain the mass of coal required.
(iii) Repeat the calculation for uranium-235 and determine the corresponding mass of nuclear fuel consumed.
(iv) Using your answers, find the ratio of the mass of coal to the mass of uranium-235 needed to produce the same annual electrical output.