Question

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

• A. $\textit{P}^{'}\textit{T}^{'}=32PT$
• B. $\textit{P}^{'}\textit{T}^{'}=16PT$
• C. $\textit{P}^{'}\textit{T}^{'}=8PT$
• D. $\textit{P}^{'}\textit{T}^{'}=4PT$

Answer 1

Answer: (A)

For a black body, wavelength for maximum intensity :
$\lambda \propto \frac{1}{\textit{T}}$ and $\textit{P} \propto \textit{T}^{4}\Rightarrow \textit{P} \propto \frac{1}{\lambda ^{4}}$
$\textit{P}^{'}=16P$
$\therefore \textit{P}^{'}\textit{T}^{'}=32PT$