Three very large plates of the same area are | vedclass

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

Question

(C) For the middle plate to be in a steady state,the net power received by the plate must equal the net power emitted by the plate.Let the temperature

Vedclass · Accepted Answer

$\left (\frac{97}{2} \right )^{1/4} T$

Vedclass · Answer

(C) For the middle plate to be in a steady state,the net power received by the plate must equal the net power emitted by the plate.Let the temperature of the middle plate be $	heta$.The power received by the middle plate from the first plate (at $2T$) and the third plate (at $3T$) is given by the Stefan-Boltzmann law for black bodies: $P_{	ext{received}} = \sigma A (2T)^4 + \sigma A (3T)^4$.The middle plate emits radiation from both its sides,so the total power emitted is: $P_{	ext{emitted}} = 2 	imes \sigma A 	heta^4$.Equating the power received and emitted:$\sigma A (2T)^4 + \sigma A (3T)^4 = 2 \sigma A 	heta^4$$16 T^4 + 81 T^4 = 2 	heta^4$$97 T^4 = 2 	heta^4$$	heta^4 = \frac{97}{2} T^4$$	heta = \left( \frac{97}{2} ight)^{1/4} T$

Similar Questions

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively,the ratio of the radii of the star $A$ and the sun is: (in $: 1$)

$A$ black body at a temperature of $127^{\circ}C$ radiates heat at the rate of $1 \ cal/cm^2 \cdot s$. At a temperature of $527^{\circ}C$,the rate of heat radiation from the body in $cal/cm^2 \cdot s$ will be:

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 $\frac {A_2}{A_1}$.

Write the value and dimensional formula of the Stefan-Boltzmann constant.

Vedclass Test Series

Exam Paper Generator

Online Exam Module