Question

A black body radiates heat energy at the rate of $2\times {10}^5{\text{J-s}}^{-1}{\text{m}}^{-2}$ at a temperature of ${127}^{\circ }\text{C}$. The temperature of black body, at which the rate of heat radiation is $32\times {10}^5{\text{J-s}}^{-1}{\text{m}}^{-2}$ is

• A. ${273}^{\circ }\text{C}$
• B. ${527}^{\circ }\text{C}$
• C. ${873}^{\circ }\text{C}$
• D. ${927}^{\circ }\text{C}$

Answer 1

The correct option is B ${527}^{\circ }\text{C}$

For a perfect black body, ${\left(\frac{T_2}{T_1}\right)}^4=\frac{E_2}{E_1}$
or $\frac{T_2}{T_1}={\left(\frac{E_2}{E_1}\right)}^{1/4}={\left(\frac{32\times {10}^5}{2\times {10}^5}\right)}^{1/4}=2$
$\therefore T_2=2T_1=2\times (127+273)=800\text{K}$
$\Rightarrow T_2=800-273={527}^{\circ }\text{C}$