The emissivity of tungsten is aproximately 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 if heat conduction along the support is neglected?`sigma=5.67xx10^-8` SI units.

Options

A. 2119.8W
B. 2019.8W
C. 2219.8 W
D. 1919.8 WS

Answer

B

Explanation

Net heat lost by sphere per second
`H_("net")=epsilonsigmaA(T^(4)-T_(0)^(4))`
Where , T= temperature of sphere = 300 K
`T_(0)` = temperature of surrounding =300 K
Area `A=4pir^(2)=4pi(0.01)^(2)`
To maintain constant temperature,
Power input required = net heat loss from the surface
`P_("input")=epsilonsigmaA(T^(4)-T_(0)^(4))`
`=0.35xx5.67xx10^(-8)xx4pi(0.01)^(2)xx(3000^(4)-300^(4))`
`P_("input")=2019.8 W`