Question

A perfectly black body emits a radiation at temperature '$T_1$' K. If it is to radiate at 16 times this power, its temperature '$T_2$' K should be

• A. $8T_1$
• B. $4T_1$
• C. $2T_1$
• D. $16T_1$

Hint:

Because power scales with the fourth power of temperature ($P \propto T^4$), doubling the absolute temperature increases the radiated power exponentially by $2^4 = 16$. This short conceptual fact lets you pick option (C) immediately!

Answer 1

The Correct Option is C

Step 1: Recall Stefan's law.
A black body radiates power proportional to the fourth power of its temperature, $P\propto T^4$.

Step 2: Set up the ratio.
\[ \frac{P_2}{P_1}=\left(\frac{T_2}{T_1}\right)^4 \] We want $P_2=16P_1$.

Step 3: Solve.
$16=\left(\frac{T_2}{T_1}\right)^4$, so $\frac{T_2}{T_1}=\sqrt[4]{16}=2$.

Step 4: State the result.
\[ T_2=2T_1 \] \[ \boxed{2T_1} \]