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

We know that: $\frac{Q}{t}=P=\sigma T^4$
So, $P\propto T^4$
If temperature changes from $T$ at power $P_1$ to $2T$ at power $P_2$ then
$\frac{P_1}{P_2}={\left(\frac{T}{2T}\right)}^4=\frac{1}{16}$

$\frac{P_2}{P_1}={\left(\frac{2T}{T}\right)}^4=\frac{16}{1}$