Question

Power emitted by a black body at temperature ${50}^{\circ }C$ is $P$. Now, temperature is doubled i.e. temperature of black body becomes ${100}^{\circ }C$. Now, power emitted is:

• A. greater than $P$ but less than $16P$
• B. greater than $16P$
• C. $P$
• D. $16P$

Answer 1

Answer: (A)

greater than $P$ but less than $16P$

Given,
temperature of black body in first condition
$T_1={50}^{\circ }C$
Emitted power in first condition, $P_1=P$
Temperature of black body in second condition
$T_2={100}^{\circ }C$
We know that,
$P\propto T^4$
Hence, $\frac{P_2}{P_1}=\frac{T_2^4}{T_1^4}$
$\Rightarrow \frac{P_2}{P}={\left(\frac{273+100}{273+50}\right)}^4$
$\Rightarrow \frac{P_2}{P}={\left(\frac{373}{323}\right)}^4$
$\frac{P_2}{P}=(1.15{)}^4$
$\frac{P_2}{P}=1.77\approx 2$
$P_2=2P$.