Two electric lamps A and B radiate the same p | vedclass

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

Question

(A) According to the Stefan-Boltzmann law,the power radiated by a body is given by $P = e A \sigma T^4$,where $e$ is the emissivity,$A$ is the surface

Vedclass · Accepted Answer

$(\frac{e_B}{e_A})^{1/4}$

Vedclass · Answer

(A) According to the Stefan-Boltzmann law,the power radiated by a body is given by $P = e A \sigma T^4$,where $e$ is the emissivity,$A$ is the surface area,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is the absolute temperature.Since both lamps radiate the same power $(P_A = P_B)$ and have the same dimensions (same surface area $A$),we have:$e_A A \sigma T_A^4 = e_B A \sigma T_B^4$Canceling the common terms $A$ and $\sigma$,we get:$e_A T_A^4 = e_B T_B^4$Rearranging the terms to find the ratio $\frac{T_A}{T_B}$:$\frac{T_A^4}{T_B^4} = \frac{e_B}{e_A}$Taking the fourth root on both sides:$\frac{T_A}{T_B} = (\frac{e_B}{e_A})^{1/4}$

Two electric lamps $A$ and $B$ radiate the same power. Their filaments have the same dimensions and have emissivities $e_A$ and $e_B$. Their surface temperatures are $T_A$ and $T_B$. The ratio $\frac{T_A}{T_B}$ will be equal to :-

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.

$A$ black rectangular surface of area $A$ emits energy $E$ per second at $27^{\circ} C$. If length and breadth are reduced to $1/3$ of their initial values and the temperature is raised to $327^{\circ} C$,then the energy emitted per second becomes:

$A$ body emits $5 \ W$ of energy at a temperature of $127^{\circ}C$. If the temperature is increased to $927^{\circ}C$,then the emitted energy becomes .......... $W$.

$A$ planet of radius $R_{p}$ is revolving around a star of radius $R^{}$ which is at temperature $T^{}$. The distance between the star and the planet is $d$. If the planet's temperature is $f T^{*}$, then $f$ is proportional to

The temperature of a spherical black body is inversely proportional to its radius. If its radius is doubled,then the power radiating from it will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module