Question

A heated body maintained at $T$ K emits thermal radiation of total energy $E$ with a maximum intensity at frequency $\nu$. The emissivity of the material is $0.5$. If the temperature of the body be increased to and maintained at temperature $3T$ K, then

• A. The maximum intensity of the emitted radiation will occur at frequency $\nu /3$
• B. The maximum intensity of the emitted radiation will occur at frequency $3\nu$
• C. The total energy of emitted radiation will become $81E$
• D. The total energy of emitted radiation will become $27E$

Answer 1

Answer: (B), (C)

The correct options are
B The maximum intensity of the emitted radiation will occur at frequency $3\nu$
C The total energy of emitted radiation will become $81E$

According to Wien's Displacement Law, ${\lambda }_{max}=\frac{b}{T}$

$⟹{\nu }_{max}=\frac{b}{cT}$

Thus, the new frequency at which maximum intensity occurs is $\frac{v}{3}$.

Also the power of emitted radiation can be written as $P=ϵ\sigma A{T}^4$.

Thus, the power becomes $(\frac{3}{1}{)}^4=81$ times the previous power.

Thus, the total energy of emitted radiation will be $81E.$