The energy spectrum of a black body has maxim | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to Wien's displacement law, $\lambda_m T = 	ext{constant}$.Let the initial temperature be $T_1$ and the final temperature be $T_2$. Giv

Vedclass · Accepted Answer

$256/81$

Vedclass · Answer

(A) According to Wien's displacement law, $\lambda_m T = 	ext{constant}$.Let the initial temperature be $T_1$ and the final temperature be $T_2$. Given $\lambda_{m1} = \lambda_0$ and $\lambda_{m2} = 3\lambda_0/4$.Using $\lambda_{m1} T_1 = \lambda_{m2} T_2$, we get:$T_2 = \frac{\lambda_{m1}}{\lambda_{m2}} T_1 = \frac{\lambda_0}{3\lambda_0/4} T_1 = \frac{4}{3} T_1$.According to the Stefan-Boltzmann law, the power radiated $P \propto T^4$.Therefore, the ratio of the powers is:$\frac{P_2}{P_1} = \left( \frac{T_2}{T_1} ight)^4 = \left( \frac{4/3 T_1}{T_1} ight)^4 = \left( \frac{4}{3} ight)^4 = \frac{256}{81}$.

The energy spectrum of a black body has maximum energy at a wavelength of $\lambda_0$. Now, the temperature of the black body is increased such that the maximum energy is obtained at a wavelength of $3\lambda_0/4$. By what factor will the power radiated by the black body increase?

Similar Questions

$A$ black sphere of radius $R$ radiates power $P$ at a certain temperature $T$. If the temperature is doubled and the radius is also doubled,the new power radiated will be: (in $P$)

$A$ wire of length $L$ and diameter $d$ is used in a bulb. The temperature of the wire is $T$ and the power radiated by the wire is $P$. Its emissivity is $e$ ($\sigma$ = Stefan's constant). (Assume that the emissivity of the wire material is the same at all wavelengths).

Obtain the equation for the rate of emission of heat for a perfect black body by using the Stefan-Boltzmann law.

$A$ black metal foil is warmed by radiation from a small sphere at temperature $T$ and at a distance $d$. It is found that the power received by the foil is $P$. If both the temperature and distance are doubled,the power received by the foil will be:

The cooling rate of a sphere at $600\,K$ in an external environment of $200\,K$ is $R$. When the temperature of the sphere is reduced to $400\,K$,the cooling rate of the sphere becomes:

Vedclass Test Series

Exam Paper Generator

Online Exam Module