Question:
A black body emits radiation of maximum intensity of wavelength '\(λ\)' at temperature 'T' K. Its corresponding wavelength at temperature \((2.5T)\) K will be
A black body emits radiation of maximum intensity of wavelength '\(λ\)' at temperature 'T' K. Its corresponding wavelength at temperature \((2.5T)\) K will be
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Thermal resistance is L over K A, so equal area and resistance make L proportional to K.
Updated On: Oct 1, 2026
- \(\frac{2λ}{3}\)
- \(\frac{2λ}{5}\)
- \(\frac{4λ}{5}\)
- \(\frac{16λ}{81}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Thermal resistance of a rod is \(R_{th} = \frac{L}{KA}\).
Step 2: Equate:
Same \(A\) and same \(R_{th}\) give \(\frac{L_1}{K_1} = \frac{L_2}{K_2}\), so \(\frac{L_1}{L_2} = \frac{K_1}{K_2} = \frac65\).
Final Answer:
The lengths are in the ratio 6:5, option (B). \[ \boxed{6:5} \]
Thermal resistance of a rod is \(R_{th} = \frac{L}{KA}\).
Step 2: Equate:
Same \(A\) and same \(R_{th}\) give \(\frac{L_1}{K_1} = \frac{L_2}{K_2}\), so \(\frac{L_1}{L_2} = \frac{K_1}{K_2} = \frac65\).
Final Answer:
The lengths are in the ratio 6:5, option (B). \[ \boxed{6:5} \]
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