Question

The temperature of a black body increases from $T$ to $2T$. The factor by which the rate of emission will increase

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is D $16$

Energy radiated per unit time is
$E=\sigma T^{4}A$ $($for black body$)$
$E\propto T^4$ $($for same black body$)$
So, we can write
$\frac{E_1}{E_2}={\left(\frac{T_1}{T_2}\right)}^4$
$\Rightarrow \frac{E_1}{E_2}={\left(\frac{T}{2T}\right)}^4=\frac{1}{16}$
$\Rightarrow E_2=16E_1$
Thus, the rate of emission will increase by factor $16$.

Why this question? Tip: For block body, power is directly proportional to the fourth power of temperature. Temperature should always be in Kelvin.