Problem

A long rod has one end at

0^\circ\text{C}

and other end at a high temperature. The coefficient of thermal conductivity varies with distance from the low temperature end as

K = K_0(1 + ax)

, where

K_0 = 10^2 \text{ SI unit}

and

a = 1 \text{ m}^{-1}

. At what distance from the first end the temperature will be

100^\circ\text{C}

? The area of cross-section is

1 \text{ cm}^2

and rate of heat conduction is

1 \text{ W}

. a. 2.7 m b. 1.7 m c. 3 m d. 1.5 m