The energy spectrum of a blackbody exhibits a maximum around a wavelength

Discussion Forum : Heat Transfer

Question -

The energy spectrum of a blackbody exhibits a maximum around a wavelength $λ_{0}$ . The temperature of the black body is now changed such that the energy is maximum around a wavelength $\frac{3 λ_{0}}{4}$ The power radiated by the blackbody will now increase by a factor:

Options:

A .

\frac{256}{81}

B .

\frac{16}{9}

C .

\frac{4}{3}

D . None

Answer: Option A
:
A

According to Wien's law wavelength corresponding to maximum energy decreases. When the temperature of blackbody increases i.e.,

$λ_{m} T = c o n s t a n t \Rightarrow \frac{T_{2}}{T_{1}} = \frac{λ_{1}}{λ_{2}} = \frac{λ_{0}}{\frac{3 λ_{0}}{4}} = \frac{4}{3}$

Now according to Stefan's law

$\frac{E_{2}}{E_{1}} = {(\frac{T_{2}}{T_{1}})}^{4} = {(\frac{4}{3})}^{4} = \frac{256}{81}$ .

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