Answer
(a) The amount of thermal energy generated each year is $~~7.56\times 10^{16}~J$
(b) The required mass of uranium is $0.84~kg$
Work Step by Step
(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 $0.84~kg$
