Question

A perfectly black body radiates power at temperature \(T_{1}\)K. If it is to radiate 16 times this power, its temperature should be increased by

• A. \((16T_{1})K\)
• B. \((4T_{1})K\)
• C. \((2T_{1})K\)
• D. \((T_{1})K\)

Hint:

Radiated power is proportional to the fourth power of temperature. Find the new temperature and subtract the old one.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
By the Stefan-Boltzmann law, the power radiated by a black body is \(P=\sigma AT^{4}\), so \(P\propto T^{4}\).

Step 2: Find the New Temperature
\(\dfrac{P_2}{P_1}=16=\left(\dfrac{T_2}{T_1}\right)^{4}\)
So \(\dfrac{T_2}{T_1}=2\) and \(T_2=2T_1\).

Step 3: Calculation
The increase is \(T_2-T_1=2T_1-T_1=T_1\).

Step 4: Compare the options
The increase of \(T_1\text{ K}\) is the last option.

Final Answer:
The temperature must be raised by T1 kelvin. \[ \boxed{\text{(D) }(T_{1})\text{ K}} \]