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 $3\times 10^{8}m{s}^{-1}$ )

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

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 $=10^{9}Watt$ .
$\frac{\Delta m}{\Delta t}=\frac{P}{c^2}=\frac{{\left(10\right)}^9}{{\left(3\times {\left(10\right)}^8\right)}^2}$
$\Rightarrow \frac{\Delta m}{\Delta t}=\frac{10^{-7}}{9}kg{s}^{-1}$
The mass of fuel consumed $perhour$ $=\frac{{\left(10\right)}^{-7}}{9}\times \left(1000g\right)\left(3600h^{-1}\right)=4\times {\left(10\right)}^{-2}g{h}^{-1}$ .