## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) The amount of thermal energy generated each year is $~~7.56\times 10^{16}~J$ (b) The required mass of uranium is $0.84~kg$
(a) We can find the number of seconds that the plant generates energy each year: $t = (0.8)(365)(24)(3600~s) = 25,228,800~s$ We can find the amount of electricity generated each year: $E_e = P\times t$ $E_e = (1000\times 10^6~W)(25,228,800~s)$ $E_e = 2.52\times 10^{16}~J$ We can find the amount of thermal energy generated each year: $E_t = 3\times E_e$ $E_t = (3)~(2.52\times 10^{16}~J)$ $E_t = 7.56\times 10^{16}~J$ The amount of thermal energy generated each year is $~~7.56\times 10^{16}~J$ (b) We can find the required mass of uranium: $E = mc^2$ $m = \frac{E}{c^2}$ $m = \frac{7.56\times 10^{16}~J}{(3.0\times 10^8~m/s)^2}$ $m = 0.84~kg$ The required mass of uranium is $0.84~kg$