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(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,$P_2 = \frac{81}{64}E$.

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