The rectangular surface of area 8 text{ cm} t | vedclass

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

Question

(D) According to Stefan-Boltzmann law,the rate of energy emission $P$ is given by $P = A \sigma T^4$,where $A$ is the area,$\sigma$ is the Stefan-Bolt

Vedclass · Accepted Answer

$\frac{81}{64}E$

Vedclass · Answer

(D) According to Stefan-Boltzmann law,the rate of energy emission $P$ is given by $P = A \sigma T^4$,where $A$ is the area,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is the absolute temperature in Kelvin.Initial state: $A_1 = 8 	ext{ cm} 	imes 4 	ext{ cm} = 32 	ext{ cm}^2$,$T_1 = 127 + 273 = 400 	ext{ K}$. Rate $P_1 = E$.Final state: Length and breadth are halved,so $A_2 = (8/2) 	ext{ cm} 	imes (4/2) 	ext{ cm} = 4 	ext{ cm} 	imes 2 	ext{ cm} = 8 	ext{ cm}^2$. Note that $A_2 = A_1 / 4$. $T_2 = 327 + 273 = 600 	ext{ K}$.Using the ratio: $\frac{P_2}{P_1} = \frac{A_2}{A_1} 	imes \left( \frac{T_2}{T_1} ight)^4$.$\frac{P_2}{E} = \frac{1}{4} 	imes \left( \frac{600}{400} ight)^4 = \frac{1}{4} 	imes \left( \frac{3}{2} ight)^4 = \frac{1}{4} 	imes \frac{81}{16} = \frac{81}{64}$.Therefore,$P_2 = \frac{81}{64}E$.

Similar Questions

If the ratio of the radii of two spheres of the same material and at the same temperature is $1:2$,find the ratio of their emissive power.

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 :-

State and explain the Stefan-Boltzmann law.

$A$ black body radiates energy at the rate of $E \text{ W/m}^2$ at a high temperature $T \text{ K}$. When the temperature is reduced to $\left(\frac{T}{2}\right) \text{ K}$, the radiant energy is

$A$ body of area $1\, cm^2$ is heated to a temperature $1000\, K$. The amount of energy radiated by the body in $1\, second$ is .......... $Joule$ (Stefan's constant $\sigma = 5.67 \times 10^{-8}\, W\, m^{-2}K^{-4}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module