Question:
If the absolute temperature of a black body is tripled, the total radiant energy emitted per second per unit area increases by a factor of:
If the absolute temperature of a black body is tripled, the total radiant energy emitted per second per unit area increases by a factor of:
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Radiation depends strongly on temperature:
\[
E \propto T^4 \Rightarrow small T change causes large energy change
\]
Updated On: Jun 10, 2026
- 3
- 9
- 27
- 81
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The Correct Option is D
Solution and Explanation
Concept:
According to Stefan-Boltzmann law:
\[
E \propto T^4
\]
Step 1: Initial and final temperature \[ T_2 = 3T_1 \]
Step 2: Ratio of emissive powers \[ \frac{E_2}{E_1} = \left(\frac{T_2}{T_1}\right)^4 = 3^4 \]
Step 3: Final result \[ 3^4 = 81 \] Thus, the radiation increases by a factor of 81.
Step 1: Initial and final temperature \[ T_2 = 3T_1 \]
Step 2: Ratio of emissive powers \[ \frac{E_2}{E_1} = \left(\frac{T_2}{T_1}\right)^4 = 3^4 \]
Step 3: Final result \[ 3^4 = 81 \] Thus, the radiation increases by a factor of 81.
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