Question

Calculate the energy emitted by the sun in one second. Also estimate the mass of the sun that is converted to energy in one second.
(Take solar constant as $1.4\times {10}^{3}W{m}^{-2}$, distance between the earth and the sun as $1.5\times {10}^{11}m$ and the velocity of light as $3\times {10}^{8}m{S}^{-1}$).

Answer 1

One square metre of the earth gets $1.4kW$ of energy in one second. The energy of the sun is spread over a spherical surface of area of $4\pi R^2$, where $R$ is the distance between the earth and the sun.
Thus, the solar energy given out by the sun, in one second
$=1.4\times {10}^3\times 4\pi R^{2}J$
$=1.4\times {10}^3\times 4\times \frac{22}{7}\times {1.5}^2\times {10}^{22}J=3.96\times {10}^{26}J$
To produce this energy, the mass of the sun used per second is
$m=\frac{c^2\times t}{E}=\frac{3.96\times {10}^{26}}{9\times {10}^{16}}=4.4\times {10}^{9}kg$
$\because E=m{c}^2$