Question

A heated body emits radiation which has maximum intensity at frequency $v_m$. If the temperature of the body is doubled:

• A. the maximum intensity radiation will be at frequency $2v_m$
• B. the maximum intensity radiation will be at frequency $\frac{1}{2}{v}_m$
• C. the total emitted energy will increase by a factor 16
• D. the total emitted energy will increase by a factor 2

Answer 1

Answer: (A), (C)

The correct options are
A the maximum intensity radiation will be at frequency $2v_m$
C the total emitted energy will increase by a factor 16

The maximum intensity of radiation occurs at a particular temperature ${\lambda }_{max}$ which is given by Wien's displacement law.



${\lambda }_{max}T=$ constant

When temperature $T$ is doubled
${\lambda }_{max}^{\prime }=\frac{{\lambda }_{max}}{2}$

Since $c=\nu \lambda$, if ${\lambda }_{max}$ is halved, frequency $\nu$ doubles.

By Stefan's law, emissive power
$P\propto T^4$.

If temperature is doubled, power $P^{\prime }=16P$. If power (energy radiated per second) becomes 16 times, total energy emitted also becomes 16 times.