Question

A heated body emits radiation which has maximum intensity near the frequency ${\nu }_0$. If the absolute temperature of the body is doubled,

• A. The maximum intensity of radiation will be near the frequency ${\nu }_0$
• B. The maximum intensity of radiation will be near the frequency $\frac{{\nu }_0}{2}$.
• C. The total energy emitted will increase by a factor of $16$
• D. The total energy emitted will increase by a factor of $8$

Answer 1

The correct option is C The total energy emitted will increase by a factor of $16$

According to Wein's displacement law,

${\lambda }_m.T=b\text{(constant)}$

$\Rightarrow {\lambda }_m\alpha \frac{1}{T}$

Where $T$ is absolute temperature and ${\lambda }_m$ is the wavelength of emitted radiation having maximum intensity.

We know that wavelength is inversely to frequency.

$\Rightarrow \nu \alpha T$

$\therefore$ If temperature is doubled, so maximum Intensity radiation frequency will also get doubled, ${\nu }_{max}\to 2{\nu }_0$.

From the Stefan's law, we know energy emitted is directly proportional to the fourth power of absolute temperature of the body.

$E\propto T^4$

So, if temperature is doubled,
$E^{\prime }\propto (2T{)}^4$

$E^{\prime }\propto 16T^4$

Thus, Energy emitted will become $16$ times.

Hence, option $\left(C\right)$ is correct.