Q: Three very large plates of same are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i. e., second) plate under steady condition is

(a) $(\frac{65}{2})^{1/4} T $

(b) $(\frac{97}{4})^{1/4} T $

(c) $(\frac{97}{2})^{1/4} T $

(d) $(97)^{1/4} T $

Ans: (c)

Sol: Let temperature of middle plate is T’

In steady state,

Energy absorbed by middle plate = Energy released by middle plate

$\large \sigma A [(3T)^4 – (T’)^4] = \sigma A [(T’)^4 – (2T)^4]$

$\large T’ = (\frac{97}{2})^{1/4} T $