A thin steel square plate of side 10 cm is h | vedclass

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(A) The rate of energy emission (power) from a black body is given by Stefan-Boltzmann Law: $P = A \varepsilon \sigma T^4$.Here,the side of the square

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$1000$

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(A) The rate of energy emission (power) from a black body is given by Stefan-Boltzmann Law: $P = A \varepsilon \sigma T^4$.Here,the side of the square plate is $s = 10 \ cm = 0.1 \ m$.The area $A = s^2 = (0.1 \ m)^2 = 0.01 \ m^2$.Since it is a plate,it emits radiation from both sides,so the total surface area is $A_{total} = 2 	imes A = 2 	imes 0.01 = 0.02 \ m^2$.Given $P = 1134 \ W$,$\sigma = 5.67 	imes 10^{-8} \ W \ m^{-2} \ K^{-4}$,and assuming $\varepsilon = 1$:$1134 = 0.02 	imes 1 	imes 5.67 	imes 10^{-8} 	imes T^4$.$T^4 = \frac{1134}{0.02 	imes 5.67 	imes 10^{-8}} = \frac{1134}{0.1134 	imes 10^{-8}} = 10^4 	imes 10^8 = 10^{12}$.$T = (10^{12})^{1/4} = 10^3 = 1000 \ K$.

$A$ thin steel square plate of side $10 \ cm$ is heated. The rate of energy emission from the heated plate is $1134 \ W$. What is the temperature of the plate in $K$? (Assume emissivity $\varepsilon = 1$ and $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

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