A long rod has one end at and the other end at a high temperature

PHYSICS · Single correct · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A long rod has one end at

0^\circ\text{C}

and the 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{W m}^{-1}\text{K}^{-1}

and

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

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

100^\circ\text{C}

? The cross-sectional area is

1\,\text{cm}^2

and the rate of heat conduction is

1\,\text{W}

. (1)

2.7\,\text{m}

(2)

1.7\,\text{m}

(3)

3\,\text{m}

(4)

1.5\,\text{m}