Question

three very large plates of same area are kept parallel and close to each other. they are considered as ideal black surfaces. they have bery high thermal conductivity. the first and third plates are maintained at temperatures 2t and 3t resp. temperature in the middle i.e. of second plate under steady state conditions is?​

Answer 1

Question:

Three very large plates of same area are kept parallel and close to each other. they are considered as ideal black surfaces. they have bery high thermal conductivity. the first and third plates are maintained at temperatures 2t and 3t resp. temperature in the middle i.e. of second plate under steady state conditions is?​

Solution:

Given,

The first and third plates are maintained at temperatures 2t and 3t resp.

We know, During steady state,

Energy absorbed by middle plate  = Energy released by middle plate.

σA(3T)^4 – σA(T’)^4 = σA(T’)^4 – σA(2T)^4

(3T)^4 – (T’)^4 = (T’)^4 – (2T)^4

(2T’)^4 = (16 + 81) T^4

$T' = \left(\dfrac{97}{2}\right)^{\frac{1}{4}} T$