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The temperature of the sun can be found out by using
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Stefan's Boltzmann law
We know solar constant (heat flux falling on the earth), $\mathrm{S}=1350 \mathrm{~W} / \mathrm{m}^2$
Let $E$ be the energy emitted by the sun per second per unit area. Then, the total energy emitted by the sun is one second $4 \pi R^2 E$. This energy is falling on a sphere of radius equal to the radius of the Earth's orbit around the sun i.e., on a sphere of surface area $4 \pi \mathrm{r}^2$.
Energy falling per unit area $=\frac{4 \pi R^2 E}{4 \pi r^2}=\frac{E R^2}{r^2}=S$
Using Stefan Boltzman's law:
$\mathrm{E}=\sigma \mathrm{T}^4$
$\mathrm{T}=\left(\frac{\mathrm{S} \times \mathrm{R}^2}{\sigma \times \mathrm{r}^2}\right)^{\frac{1}{4}}=5760 \mathrm{~K}$
Let $E$ be the energy emitted by the sun per second per unit area. Then, the total energy emitted by the sun is one second $4 \pi R^2 E$. This energy is falling on a sphere of radius equal to the radius of the Earth's orbit around the sun i.e., on a sphere of surface area $4 \pi \mathrm{r}^2$.
Energy falling per unit area $=\frac{4 \pi R^2 E}{4 \pi r^2}=\frac{E R^2}{r^2}=S$
Using Stefan Boltzman's law:
$\mathrm{E}=\sigma \mathrm{T}^4$
$\mathrm{T}=\left(\frac{\mathrm{S} \times \mathrm{R}^2}{\sigma \times \mathrm{r}^2}\right)^{\frac{1}{4}}=5760 \mathrm{~K}$
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