Question

We have three identical perfectly black plates. The temperatures of first and third plate is T and 3T. What is the temperature of second plate if system is in equilibrium?

Options

• 41^1/4T

• 51^1/4T

• 2^1/4T

• 37^1/4T

Answer 1

41^1/4T

Explanation:

Power of plate 1 : A σ T⁴

Power of plate 3 : 81 A σ T⁴

∴ Power absorbed by Middle plate `("A"sigma"T"^4)/2 + (81  "A"  sigma  "T"^4)/2` = 41 A σ T⁴ Power emitted by middle plate; σ A(x)⁴

At steady state

 σ A(x)⁴ = 41 A σ T⁴ 

x = 41^1/4 T