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Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black
\( \mathrm{P} \) surfaces and have very high thermal conductivity. The first

W and third plates are maintained at temperatures \( 2 T \) and \( 3 T \) respectively. The temperature of the middle (i.e. second) plate under steady state condition is [IIT JEE 2012]
(a) \( \left(\frac{65}{2}\right)^{\frac{1}{4}} T \)
(b) \( \left(\frac{97}{4}\right)^{\frac{1}{4}} T \)
(c) \( \left(\frac{97}{2}\right)^{\frac{1}{4}} T \)
(d) \( (97)^{\frac{1}{4}} T \)
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