Question

How much mass has to be converted into energy to produce electric power of $500\, MW$ for one hour?

• A. $2\times10^{-5}\,kg$
• B. $1\times10^{-5}\,kg$
• C. $3 \times10^{-5}\,kg$
• D. $4 \times10^{-5}\,kg$

Answer 1

Answer: (A)

Here, $P = 500\,MW$
$=5\times 10^{8}\,W,t=1\,h=3600\,s$
Energy produced, $E=P\times t=5\times10^{8}\times3600=18\times10^{11}\,J$
As $E=mc^{2}$
$\therefore m=\frac{E}{c^{2}}$
$=\frac{18\times10^{11}}{\left(3\times10^{8}\right)^{2}}$
$=\frac{18\times10^{11}}{9\times10^{16}}$
$=2\times10^{-5}\,kg$