Three identical flat sheets (i.e., area and shape are the same) of a very thin m

Question

Three identical flat sheets (i.e., area and shape are the same) of a very thin material are stacked on top of one another but spaced in such a way that they are parallel but are held slightly apart. There is no thermal energy transfer by either conduction or convection. However each sheet absorbs and radiates energy like a perfect blackbody. The top sheet is at 300 K and the bottom sheet is at 100 K. The middle sheet absorbs all of the radiant energy incident on it from the bottom facing side of the top sheet (and none from the upward facing side of the top sheet) and from the top facing side of the bottom sheet (and none from the downward facing side of the bottom sheet). What must be the temperature of the middle sheet if it is in thermal equilibrium (i.e., at constant temperature; energy absorbed equals energy radiated per unit time)?

106 K

197 K

214 K

253 K

301 K

106 K

197 K

214 K

253 K

301 K

Explanation / Answer

To be at thermal equilibrium with both the top and the bottom sheet:

Since the middle sheet absorbs heat of 300 K form the top sheet and 100 K from the bottom sheet, it follows that, the middle sheet should be at 197 k

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