A conductor in the shape of a cylinder of length `l` and cross sectional radius `r` is connected to a cell of emf `V`. The resistivity of the material of the conductor is `rho` and does not change much with temperature. The emissivity of the curved surface of the conductor is `e`. [Take emissivity of the flat circular surfaces to be zero]. In steady state the temperature of the conductor is `T` when the environmental temperature is `T_(0)`. The difference between `T and T_(0)` is much smaller than the environmental temperature. Stefan’s Constant is `sigma`.
Find the steady state temperature `T` for the conductor.

Answer

`T=T_(0)+(V^(2)r)/(8esigmarhol^(2)T_(0)^(3))`