Question:
The initial and the final temperatures of a black body are $27^\circ C$ and $177^\circ C$ respectively. The increase in the amount of radiation emitted per second is:
The initial and the final temperatures of a black body are $27^\circ C$ and $177^\circ C$ respectively. The increase in the amount of radiation emitted per second is:
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Remember, the Stefan-Boltzmann law relates the power radiated to the fourth power of the temperature. This relationship is key for solving radiation problems.
Updated On: May 5, 2026
506.25%
150.25%
225.75%
406.25%
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The Correct Option is D
Solution and Explanation
- By Stefan–Boltzmann law: \[ I \propto T^4 \]
- Ratio of radiations: \[ \frac{I_2}{I_1} = \left(\frac{T_2}{T_1}\right)^4 \]
- Converting temperatures to Kelvin: \[ T_1 = 300\,K,\quad T_2 = 450\,K \]
- Substituting: \[ \frac{I_2}{I_1} = \left(\frac{450}{300}\right)^4 = \left(\frac{3}{2}\right)^4 = \frac{81}{16} \]
- Increase in radiation: \[ \frac{I_2 - I_1}{I_1} = \frac{81}{16} - 1 = \frac{65}{16} \]
- Percentage increase: \[ \frac{65}{16} \times 100 = 406.25\% \]
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