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Q.

A black body emits radiation at the rate P when its temperature is T. At this temperature the wavelength at which the radiation has maximum intensity is $λ_{0} .$ If at another temperature T’ the power radiated is P’ and wavelength at maximum intensity is $λ_{0} / 2$ then

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a

$P' T' = 32 P T$

b

$P' T' = 16 P T$

c

$P' T' = 8 P T$

d

$P' T' = 4 P T$

answer is A.

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Detailed Solution

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For a black body, wavelength for maximum intensity :

$λ α \frac{1}{T} (Wien's law)$

$And P \propto T^{4} (Stefan's law)$

$\Rightarrow P α \frac{1}{λ^{4}} \Rightarrow P^{'} = 16 P$

$∴ P^{'} T^{'} = 32 P T .$

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A black body emits radiation at the rate P when its temperature is T. At this temperature the wavelength at which the radiation has maximum intensity is λ0. If at another temperature T’ the power radiated is P’ and wavelength at maximum intensity is λ0/2 then