Question

a) (15 p) We consider a nuclear reactor of power output P-1000 Megawatt (1000 million watts) electric, functioning with Plutonium. It is fueled, initially, with 1000 kg of Plutonium. The nuclear material in question is made of Plutonium nuclei, each 239 consisting in 94 protons and 239-94-145 neutrons, which is denominated by the symbol 94 Pu For thermodynamical reasons, only 1/3 of the nuclear energy in the form of heat produced by the reactor, can be converted into electricity. How much mass deficit Am should the nuclear fuel of concern delineates, if the reactor is operated through a period of At=2 years. You are supposed to use Einstein's relationship AE=C Am (where c is the velocity of light in vacuum, i.e. about 300 000 km/s). Note further that the reactor power, by definition, is given by AE/At. Make sure that you use coherent units. b) (10 p) How much mass deficit between the reactants (CO2) and the reaction products (CO2), all weighed at rest, would delineate a coal (C) thermal plant of the same capacity, working under the same thermodynamical regime, through the same period of 2 years of operation, but which needs to burn about 3 millions coal per year?

Answer 1

Power of nuclear reactor = 1000 MW = 10⁹ W = 10⁹ J / s

If thermodynamic efficiency is 33.33 % , then required nuclear energy = 3 $\times$ 10⁹ J/s

Nuclear energy required per year = 3 $\times$ 10⁹ J/s $\times$ 3.154 $\times$ 10⁷ s / year = 9.462 $\times$ 10¹⁶ J

Nuclear energy required per 2 years = 2 $\times$ 9.462 $\times$ 10¹⁶ = 18.924 $\times$ 10¹⁶ J ..............(1)

Mass deficit $\Delta$ m to generate nuclear energy as given in above eqn.(1) is calculated

from Einstein's relation , E = $\Delta$ m c²

Hence mass deficit to generate nuclear energy as given in above eqn.(1) is calculated as

$\Delta$m of Plutonium = ( 18.924 $\times$ 10¹⁶ ) / ( 9 $\times$ 10¹⁶ ) = 2.103 kg

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Oxidation reaction of Carbon and Oxygen gives 394 kJ / mole . If we consider 1 mole of carbon as 12 g , this thermal energy release in oxidation reaction of Carbon and oxygen is 32.833 MJ / kg

If a thermal power plant has operated for 2 years to generate thermal energy as given in eqn.(1) , then amount of coal to be burnt is calculated as follows

$\Delta$m of Carbon = ( 18.924 $\times$ 10¹⁶ ) / ( 32.833 $\times$ 10⁶ ) = 5.764 $\times$ 10⁹ kg