(C) Given that the total radiant power emitted by both bodies is the same: $P_A = P_B$.According to the Stefan-Boltzmann Law,$P = e \sigma A T^4$.Sinc

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

(C) Given that the total radiant power emitted by both bodies is the same: $P_A = P_B$.According to the Stefan-Boltzmann Law,$P = e \sigma A T^4$.Since $A_A = A_B$ and $\sigma$ is a constant,we have $e_A T_A^4 = e_B T_B^4$.Rearranging for $T_B$: $T_B = T_A \left( \frac{e_A}{e_B} \right)^{1/4}$.Substituting the given values: $T_B = 5802 \times \left( \frac{0.01}{0.81} \right)^{1/4}$.$T_B = 5802 \times \left( \frac{1}{81} \right)^{1/4} = 5802 \times \frac{1}{3} = 1934 \ K$.

Class 11 Physics 10-2.Heat Transfer Radiation by Stefan's Boltzmann Law

Medium

Two bodies $A$ and $B$ have emissivities of $0.01$ and $0.81$ respectively. The outer surface areas of both bodies are the same. Both bodies emit total radiant power at the same rate. The wavelength $\lambda_B$ corresponding to the maximum spectral radiance for body $B$ is $1.0 \mu m$. If the temperature of body $A$ is $5802 \ K$,then the temperature of body $B$ is .... $K$.

A
$1526$
B
$1349$
C
$1934$
D
$1589$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

10-2.Heat Transfer

Subtopic

Radiation by Stefan's Boltzmann Law

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on Earth at a distance $r$ from the Sun. Where $r_0$ is the radius of the Earth and $\sigma$ is Stefan's constant.

MediumAIEEE 2006

View Solution

The radiant energy from the sun incident normally at the surface of the earth is $20 \, kcal/(m^2 \cdot min)$. What would have been the radiant energy incident normally on the earth,if the sun had a temperature twice of the present one? (in $kcal/(m^2 \cdot min)$)

MediumAIPMT 1998

View Solution

The temperature of a perfect black body is $727^{\circ}C$ and its surface area is $0.1\, m^{2}$. If the Stefan-Boltzmann constant is $\sigma = 5.67 \times 10^{-8} \, W/m^{2} \cdot K^{4}$,then the heat radiated in $1\, min$ is ........ $cal$.

Medium

View Solution

$A$ spherical black body with a radius of $24\;cm$ radiates $440\;W$ power at $500\;K$. If the radius were halved and the temperature doubled,the power radiated in watt would be

MediumIIT 1997

View Solution

The energy emitted per second by a black body at $27^{\circ}C$ is $10\;J$. If the temperature of the black body is increased to $327^{\circ}C$,the energy emitted per second will be ......... $J$.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on Earth at a distance $r$ from the Sun. Where $r_0$ is the radius of the Earth and $\sigma$ is Stefan's constant.

The radiant energy from the sun incident normally at the surface of the earth is $20 \, kcal/(m^2 \cdot min)$. What would have been the radiant energy incident normally on the earth,if the sun had a temperature twice of the present one? (in $kcal/(m^2 \cdot min)$)

The temperature of a perfect black body is $727^{\circ}C$ and its surface area is $0.1\, m^{2}$. If the Stefan-Boltzmann constant is $\sigma = 5.67 \times 10^{-8} \, W/m^{2} \cdot K^{4}$,then the heat radiated in $1\, min$ is ........ $cal$.

$A$ spherical black body with a radius of $24\;cm$ radiates $440\;W$ power at $500\;K$. If the radius were halved and the temperature doubled,the power radiated in watt would be

The energy emitted per second by a black body at $27^{\circ}C$ is $10\;J$. If the temperature of the black body is increased to $327^{\circ}C$,the energy emitted per second will be ......... $J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module