Question

The temperature at which a perfect black body radiates at the rate of $5.67\, W$ $cm^{-2}$ is (Stefan's constant is $5.67 \times10^{-8 }Js^{-1}m^{-2} K^{-4}$ .)

• A. 1000 K
• B. 2000 K
• C. 109.2 K
• D. 3388 K.

Answer 1

Answer: (A)

$E=5.67\,W\,cm^{-2}=5.67\times10^{+4}Wm^{-2};$
$\sigma=5.67\times10^{-8}Js^{-1}m^{-2}k^{-4}$
$Using\,E=\sigma\,T^4;T^4=\frac{E}{\sigma}\,or$
$T=(\frac{E}{\sigma})^{1/4}=\left(\frac{5.67\times 10^{-8}}{5.67\times10^{+4}}\right)^{1/4}=(10^{12})^{1/4}=1000\,K$