Two black spheres P and Q have radii in the r | vedclass

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

Question

(A) According to Wien's displacement law, $\lambda_m T = 	ext{constant}$, so $T \propto \frac{1}{\lambda_m}$.Given the ratio of wavelengths $\frac{\l

Vedclass · Accepted Answer

$\frac{625}{144}$

Vedclass · Answer

(A) According to Wien's displacement law, $\lambda_m T = 	ext{constant}$, so $T \propto \frac{1}{\lambda_m}$.Given the ratio of wavelengths $\frac{\lambda_P}{\lambda_Q} = \frac{4}{5}$, the ratio of temperatures is $\frac{T_P}{T_Q} = \frac{\lambda_Q}{\lambda_P} = \frac{5}{4}$.The power radiated by a black body is given by Stefan-Boltzmann law: $E = \sigma A T^4 = \sigma (4 \pi r^2) T^4$.Thus, the ratio of power radiated is $\frac{P_P}{P_Q} = \left( \frac{r_P}{r_Q} ight)^2 \left( \frac{T_P}{T_Q} ight)^4$.Substituting the given values: $\frac{r_P}{r_Q} = \frac{4}{3}$ and $\frac{T_P}{T_Q} = \frac{5}{4}$.$\frac{P_P}{P_Q} = \left( \frac{4}{3} ight)^2 	imes \left( \frac{5}{4} ight)^4 = \frac{16}{9} 	imes \frac{625}{256} = \frac{625}{9 	imes 16} = \frac{625}{144}$.

Two black spheres $P$ and $Q$ have radii in the ratio $4:3$. The wavelengths of maximum intensity of radiation are in the ratio $4:5$ respectively. The ratio of radiated power by $P$ to $Q$ is

Similar Questions

The unit of Stefan-Boltzmann's constant $(\sigma)$ is:

The ratio of the energy of emitted radiation of a black body at $27^{\circ}C$ and $927^{\circ}C$ is:

The spectrum of a black body at two temperatures $27\,^oC$ and $327\,^oC$ is shown in the figure. Let $A_1$ and $A_2$ be the areas under the two curves respectively. Find the value of $\frac {A_2}{A_1}$.

Three large identical plates are kept parallel to each other. The outer two plates are maintained at temperatures $T$ and $2T$, respectively. The temperature of the middle plate in steady state will be close to ........... $T$.

Which of the following helps us in the determination of the temperature of the sun?

Vedclass Test Series

Exam Paper Generator

Online Exam Module