Question

Three very large plates of same area 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 state condition is

• A. $\bigg(\frac{65}{2}\bigg)^4 T$
• B. $\bigg(\frac{97}{4}\bigg)^{\frac{1}{4}} T$
• C. $\bigg(\frac{97}{2}\bigg)^{\frac{1}{4}} T$
• D. $(97)^4 T$

Answer 1

Answer: (C)

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

Answer 2

Let temperature of middle plate in steady state is T$_0$ $\, \, \, Q_1 =Q_2$ $\, \, \, \, \, \, Q =$ net rate of heat flow $\therefore \, \, \, \, \sigma A (3 T)^4 - \sigma A T_0^4 =\sigma A T_0^4 - \sigma AT_0^4 -\sigma A(2T)^4$ Solving this equation, we get $\, \, \, \, \, \, \, \, \, \, \, T_0 =\bigg(\frac{97}{2}\bigg)^{1/4}T$