Question

A black body at a temperature of ${327}^{\circ }\text{C}$ radiates $4{\text{cal cm}}^{-2}{\text{s}}^{-1}$ at a temperature of ${927}^{\circ }\text{C}$, the rate of heat radiated per unit area in ${\text{cal cm}}^{-2}{\text{s}}^{-1}$ will be

• A. $16$
• B. $32$
• C. $64$
• D. $128$

Answer 1

The correct option is C $64$

Here, $T_1={327}^{\circ }\text{C}=(327+273)\text{K}=600\text{K}$ and $T_2={927}^{\circ }\text{C}=(927+273)\text{K}=1200\text{K}$
According to Stefan's law
$E\propto T^4$
$\frac{E_2}{E_1}={\left(\frac{T_2}{T_1}\right)}^4={\left(\frac{1200}{600}\right)}^4=16$
$E_2=16E_1=16\times 4=64{\text{cal cm}}^{-2}{\text{s}}^{-1}$