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# The emissivity of tungsten is approximately 0.35 A tungsten sphere 1 cm in radius is suspended within a large evacuated enclosure whose walls are at 300 K. What power input is required to maintain the sphere at a temperature of 3000 K? ( $\sigma = 5.67 \times 10 - 8$ inSI unit) A) 1020 W B) 2020 W C) 3020 W D) 4020 W

Last updated date: 14th Sep 2024
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Hint: Amount of heat radiated by tungsten will be equal to the amount of energy supplied. According to Stephan’s law the heat loss is given by, $e\sigma A({T^2} - {T_0}^2)$ . Substitute the values of initial and final temperature, area, emissivity and the constant. Simplify to find the value power required.
$Heat\,lost\,of\,radiation = e\sigma A({T^2} - {T_0}^2) \\ T = 3000k \\ {T_0} = 300k \\ A = 4\pi {r^2} = 4\pi \times {0.01^2} \\ Substituting, \\ P = 0.35 \times 5.67 \times {10^{ - 8}} \times 4\pi {(0.01)^2}[{3000^2} - {300^2}] \\ P = 2019.8W \\$
$E \propto {T^4} \Rightarrow E = \sigma {T^4}$