Question

A heated body emits radiation which has maximum intensity at frequency $v_m$. If the temperature of a 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 of $16$
• D. the total emitted energy will increase by a factor of $2$

Answer 1

Answer: (A), (C)

the maximum intensity radiation will be at frequency $2v_m$
the total emitted energy will increase by a factor of $16$

We know that from wein"s displacement law.

${\lambda }_{max}T=constant$------------(1)

Also, we know that, $velocity=frequency\times wavelength$

So, we can get $f\propto \frac{1}{\lambda }$[keeping the velocity constant]

By putting in equation (1), we will find $\frac{T}{f}=constant$, where $f=v_m$

Hence, we can say that $T=f$, so by increasing the magnitude of temperature twice, simultaneously frequency will also be increased with an equal magnitude.

Also, we know that energy emitted by any body is given as: $E=\sigma T^4$, where $\sigma =Stefan-BoltzmannConstant$

$E\propto T^4$, $E=(2T{)}^4=(16T^4)$