Three identical large metal plates are kept parallel and close to each other. Each plate can be treated as an ideal black body and has very high thermal conductivity. The first and third plates are maintained at high temperature $$T_1 = 3T$$ and $$T_3 = 2T$$. The temperature $$T_2$$ of the middle, that is second, plate under steady state condition is

A

$$\frac{5T}{2}$$

B

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

C

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

D

$$\left(\frac{65}{4}\right)^{1/4}T$$