If the radius of a star is \(R\) and it acts as a black body, what would be the temperature of the star at which the rate of energy production is \(Q\)?
1. \(\frac{Q}{4\pi R^2\sigma}\)
2. \(\left(\frac{Q}{4\pi R^2\sigma}\right )^{\frac{-1}{2}}\)
3. \(\left(\frac{4\pi R^2 Q}{\sigma}\right )^{\frac{1}{4}}\)
4. \(\left(\frac{Q}{4\pi R^2 \sigma}\right)^{\frac{1}{4}}\)

A spherical black body with a radius of 12 cm radiates 450-watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watts would be:

If the sun’s surface radiates heat at $6.3\times {10}^7$ ${\mathrm{Wm}}^{-\mathrm{2 }}$then the temperature of the sun, assuming it to be a black body, will be:
$\left(\mathrm{\sigma }=5.7\times {10}^{-8}\right)$ ${\mathrm{Wm}}^{-2}{\mathrm{K}}^{-4}$
1. $5.8\times {10}^3$ $\mathrm{K}$
2. $8.5\times {10}^3$ $\mathrm{K}$
3. $3.5\times {10}^8$ $\mathrm{K}$
4. $5.3\times {10}^8$ $\mathrm{K}$