Three large discs have same area. They are kept at equidistant in parallel. They can be considered as perfect black bodies and their thermal conductivity is very large. If temperature of first and third discs are `2T C` and `3T C` respectively then temperature of second disc in thermal steady state is . . . . .

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

As system is in thermal steady state, heat transfer rate if first and third discs are same.

`:.esigmaA[(3T)^(4)-T_(x)^(4)]=esigmaA[T_(x)^(4)-(2T)^(4)]`
`:.81T^(4)-T_(x)^(4)=T_(x)^(4)-16T^(4)`
`:.97T^(4)=2T_(x)^(4)`
`:.T_(x)^(4)=(97T^(4))/(2)`
`:.T_(x)=((97)/(2))^(1/4)T`