Question

two ends of a rod of non uniform area of cross section are maintained at temperature t1 and t2 if l is heat through conductor at distance x from left side then what is variation of l with x

Answer 1

Let Temperature at x distance from left side of conductor is T

according to formula,

$\frac{dQ}{dt}=\frac{KA\Delta T}{L}$

where, K is thermal conductivity, A is cross section area, ∆T is temperature change through ends of conductor and L is length of conductor.

now, heat flows through whole wire = heat flows through left end to x distance + heat flows through right end to (L-x) distance

KA(t1-t2)/L = KA(t1-T)/x + KA(T-t2)/(L - x) [ we assume t1 > t2 ]

or, (t1 - t2)/L = (t1 - T)/x + (T-t2)/(L - x) this is required expression.