In the core of a nuclear reactor, the mass of fuel decreases at a rate of 9.0 x 10^-6 kg hour^-1 due to nuclear reactions - AQA - A-Level Physics - Question 30 - 2021 - Paper 2

In nuclear reactions, the energy released can be calculated using Einstein's equation: $E = mc^2$ Where:

• $E$ is the energy released,
• $m$ is the mass of fuel lost (in kg),
• $c$ is the speed of light ($3.0 \times 10^8$ m/s).

Using the mass loss rate calculated above:

$E = 2.5 \times 10^{-9} \text{ kg/s} \times (3.0 \times 10^8 ext{ m/s})^2 = 2.25 \times 10^{10} \text{ J/s}$

The power output of the reactor is equal to the energy released per second. Hence, the maximum power output is:

$P = 2.25 \times 10^{10} \text{ W}$.

This is equivalent to $2.25 \times 10^{10}$ W, which is closest to the multiple-choice option C: $8.1 \times 10^{11}$ W.