Question

If the radius of a star R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?
($\sigma$ for stefan's constant.)

• A. $\left(\frac{4\pi R^{2}Q}{\sigma }\right)$ ${}^1{}^{/}{}^4$
• B. $\left(\frac{Q}{4\pi R^2\sigma }\right)$ ${}^1{}^{/}{}^4$
• C. $\frac{Q}{4\pi R^2\sigma }$
• D. $\left(\frac{Q}{4\pi R^2\sigma }\right)$ ${}^{-}{}^1{}^{/}{}^4$

Answer 1

The correct option is B $\left(\frac{Q}{4\pi R^2\sigma }\right)$ ${}^1{}^{/}{}^4$

We know that

$\sigma A{T}^4=$ rate at which black body absorbs energy

Q= rate of energy production (given)

at equilibrium

$\sigma A{T}^4=Q$

where $A=4\pi r^2$

$⟹T=(\frac{Q}{\sigma 4\pi r^2}{)}^{1/4}$

answer B