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

Options

A. `((65)/(2)) ^( 1//4) T`
B. `((97)/( 4)) ^(1//4) T`
C. `(( 97)/( 2)) ^( 1//4) T`
D. `(97) ^( 1//4) T`

Answer

C

Explanation

Let temperature of middle plate is given by, T.
Use the condition of steady heat flow,`implies sigma A ( 2 T ) ^(4) + sigma A ( 3 T ) ^(4) = sigma 2 A (T .) ^(4),`
where ` sigma,` A represents Stefan.s constant, area of cross-section .
`implies ( 2 T) ^(4) + ( 3 T) ^(4) = 2 ( T.) ^(4)`
`implies 16 T ^(4) + 81 T ^(4) = 2 ( T.) ^(4)`
`implies 97 T ^(4) = 2 ( T.) ^(4)`
`implies (T.) ^(4) = ( 97)/(2) T ^(4)`
`therefore T . = ((97)/(2)) ^(1//4)T`