Question

Imagine that a reactor converts all the given mass into energy and that it operates at a power level of $10^{9}Watt$ . The mass of the fuel consumed $perhour$ , in the reactor, will be:
(velocity of light, $c$ is $3\times 10^{8}ms^{- 1}$ )

• A. $6.6\times 10^{- 5} \, g$
• B. $0.96 \, g$
• C. $4\times 10^{- 2 \, }g$
• D. $0.8 \, g$

Answer 1

Answer: (C)

Power of reactor, $P=\frac{E}{\Delta t}=\frac{\Delta m c^{2}}{\Delta t}$ (From mass-energy equivalence equation)
Given in the problem power level $=10^{9}Watt$ .
$\frac{\Delta m}{\Delta t}=\frac{P}{c^{2}} \, =\frac{\left(10\right)^{9}}{\left(3 \times \left(10\right)^{8}\right)^{2}}$
$\Rightarrow \, \frac{\Delta m}{\Delta t}=\frac{10^{- 7}}{9} \, kgs^{- 1} \, $
The mass of fuel consumed $perhour$ $=\frac{\left(10\right)^{- 7}}{9}\times \left(1000 g\right)\left(3600 \, h^{- 1}\right)=4\times \left(10\right)^{- 2}gh^{- 1}$ .