Question

What is the power output of the sun if $4\times {10}^{9}kg$ of matter per second is converted into energy in the sun?

Use $E=m{c}^2$, where $c=3\times {10}^{8}m/s$

Answer 1

Step 1: Given data

Mass, $m=4\times {10}^{9}kg$

Speed of light, $c=3\times {10}^{8}m/s$

Time is $t=1\sec$

Step 2: Calculating energy

Einstein’s relation is given as,

$E=m{c}^2$

Where, $E$ is energy, $m$ is mass and $c$ is the speed of light

Substituting the given values in the above equation, we get,

$\begin{array}{l}E=\left(4\times {10}^{9}kg\right){\left(3\times {10}^{8}m/s\right)}^2\\ E=\left(4\times {10}^9\right)\left(3\times {10}^8\right)\left(3\times {10}^8\right)\\ E=36\times {10}^{25}\\ E=3.6\times {10}^{26}J\end{array}$

Step 3: Calculating power

Power is given as,

$P=\frac{E}{t}$

where, $E$ is energy, $t$ is time

Substituting the known values in the above equation, we get,

$\begin{array}{l}P=\frac{3.6\times {10}^{26}J}{1s}\\ P=3.6\times {10}^{26}J/s\text{or}3.6\times {10}^{26}W\end{array}$

Therefore, power output of the sun is $3.6\times {10}^{26}W$.