A rod of length with a thermally insulated lateral surface consists of a material…

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A rod of length

l

with a thermally insulated lateral surface consists of a material whose thermal conductivity varies with temperature as

k=\frac{a}{T}

, where

a

is a constant. The ends of the rod are kept at temperatures

T_1

and

T_2

. Find

T(x)

, where

x

is the distance from the end whose temperature is

T_1