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The emissivity of tungsten is 0.400. A tungsten sphere with a radius of 1.45 cm is suspended within a large evacuated enclosure whose walls are at 320 K. What power input is required to maintain the sphere at a temperature of 3000 K if heat conduction along the supports is negligible?

Respuesta :

Answer:

4850.62 Watt

Explanation:

e = 0.4

radius, r = 1.45 cm = 0.0145 m

To = 320 K

T = 3000 k

According to the Stefan's Boltzmann law

Energy radiated per unit time is given by

[tex]E = \sigma Ae\left ( T^{4}-T_{0}^{4} \right )[/tex]

where, σ is the Stefan's constant, A be the area of sphere and e be the emmisivity.

[tex]\sigma = 5.67\times 10^{-8} W/m^{2}k^{4}[/tex]

So, Power radiated is energy radiated per second

[tex]E = 5.67\times10^{-8}\times4\times3.14\times0.0145\times0.0145\times0.4\times\left ( 3000^{4}-320^{4}\right )[/tex]

E = 4850.62 Watt

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