Question

Calculate the temperature at which a perfect black body radiates at the rate of $1 \, W \, cm^{- 2}$ , Value of Stefan's constant, $\sigma =5.67\times 10^{- 5} \, erg \, s^{- 1} \, cm^{- 1} \, K^{- 4}$ .

• A. $576K$
• B. $648K$
• C. $695K$
• D. $766K$

Answer 1

Answer: (B)

Here, $\sigma =5.67\times 10^{- 5}ergs^{- 1}cm^{- 1}K^{- 4}$ ;
$E=1Wcm^{- 2}=10^{7}ergs^{- 1}cm^{- 2}$
Let $T$ be the temperature of the perfect black body.
​ Now, $E =\sigma T ^{4} \quad$ or $\quad T =\left(\frac{ E }{\sigma}\right)^{1 / 4}$
$\therefore \quad T=\left(\frac{10^{7}}{5.67 \times 10^{-5}}\right)^{1 / 4}=648 K$