Question:
The temperature of the black body increases from \(T\) to \(2T\). The factor by which the rate of emission will increase is
The temperature of the black body increases from \(T\) to \(2T\). The factor by which the rate of emission will increase is
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Stefan-Boltzmann constant \(\sigma = 5.67 \times 10^{-8}\) W m\(^{-2}\) K\(^{-4}\).
Updated On: Apr 23, 2026
- 4
- 2
- 16
- 8
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Stefan-Boltzmann law: \(E = \sigma T^4\). Rate of emission \(\propto T^4\).
Step 2: Detailed Explanation:
\(\frac{E_2}{E_1} = \left(\frac{T_2}{T_1}\right)^4 = \left(\frac{2T}{T}\right)^4 = 2^4 = 16\).
Step 3: Final Answer:
Thus, rate of emission increases by factor 16.
Stefan-Boltzmann law: \(E = \sigma T^4\). Rate of emission \(\propto T^4\).
Step 2: Detailed Explanation:
\(\frac{E_2}{E_1} = \left(\frac{T_2}{T_1}\right)^4 = \left(\frac{2T}{T}\right)^4 = 2^4 = 16\).
Step 3: Final Answer:
Thus, rate of emission increases by factor 16.
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