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A Copper Sphere is Suspended in an Evacuated Chamber Maintained at 300 K. the Sphere is Maintained at a Constant Temperature of 500 K by Heating It Electrically. - Physics

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Question

A copper sphere is suspended in an evacuated chamber maintained at 300 K. The sphere is maintained at a constant temperature of 500 K by heating it electrically. A total of 210 W of electric power is needed to do it. When the surface of the copper sphere is completely blackened, 700 W is needed to maintain the same temperature of the sphere. Calculate the emissivity of copper.

Solution

According to Stefan,s law,

power` = eAσ (T^4 - T_0^4)`

Temperature difference = 200 K

Let the emissivity of copper be e.

210 = eAσ(5004 − 3004)   ...(1)

When the surface of the copper sphere is completely blackened, 700 W is needed to maintain the temperature of the sphere.
For a black body,

= 1

700 = 1·(5004 − 3004)   ...(2)

On dividing equation (1) by equation (2) we have,
`200/700 = e/1`

⇒ e = 0.3  

  Is there an error in this question or solution?

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Solution A Copper Sphere is Suspended in an Evacuated Chamber Maintained at 300 K. the Sphere is Maintained at a Constant Temperature of 500 K by Heating It Electrically. Concept: Qualitative Ideas of Blackbody Radiation.
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