Question

The original temperature of a black body is $727^{\circ }C$ . The temperature at which this black body must be raised so as to double, the total radiant energy, is

• A. 971 K
• B. 1190 K
• C. 2001 K
• D. 1458 K

Answer 1

Answer: (B)

Using the Stefan's law, the total radiant energy is
$\theta =eA\sigma T^{4}t\propto T^4$
hence $\frac{E_2}{E_1}=\frac{T_2^4}{T_1^4}$
$={\left(\frac{T_2}{T_1}\right)}^4$
here $\frac{E_2}{E_1}=2$
$T_1=727^{\circ }C+273=1000K$
$2^{1/4}=\frac{T_2}{1000}$
or $T_2=1000\times 2^{1/4}=1000\times 1.19$
$=1190K$