Question

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 consisting in 94 protons and 239-94=145 neutrons, which is denominated by the symbol ₉₄Pu²³⁹. For thermodynamical reasons, only 1/3^rd of the nuclear energy in the form of heat produced by the reactor, can be converted into electricity. How much mass deficit Δm should the nuclear fuel of concern delineates, if the reactor is operated through a period of Δt=2 years. You are supposed to use Einstein’s relationship ΔE=c²Δm (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 ΔE/Δt.Make sure that you use coherent units.

b) How much mass deficit between the reactants (C+O₂) 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

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a) Power P=1000 x 100 watts Mass of plutonium initially m= 1000 kg Total elechical energy produced in 2 years. time t=2*365* 86400 = 6.307 x 107 sec. Electrical en energy produced te= Pxt Fe = 1000 8100 X 6.307 x 107: 6.307 X106 J Nuclear energy required 3x be = 3x6.307 xid'6 = 18.97X10'6J Mass deficit EN EN Am = C2 16 2.109 Am 18.98XI0 (3x108) b) 16 & Energy released by burning of 1 kg coal is E = 3 X107J Energy required EN=18.92 x1065 Mass of coal EN 18.92 x10 3 x107 ms 6. 3x109 mg (in 9 years) ma