One end of a thermally insulated rod is kept at a temperature $T_{1}$ and the other at $T_{2}$ . The rod is composed of two sections of lengths $l_{1}$ and $l_{2}$ and thermal conductivities $K_{1}$ and $K_{2}$ respectively. The temperature at the interface of two sections is :

$\frac{K_{1} l_{2} T_{1} + K_{2} l_{1} T_{2}}{K_{1} l_{2} + K_{2} l_{1}}$
$\frac{K_{2} l_{1} T_{1} + K_{1} l_{2} T_{2}}{K_{2} l_{1} + K_{1} l_{2}}$
$\frac{K_{1} l_{1} T_{1} + K_{2} l_{2} T_{2}}{K_{1} l_{1} + K_{2} l_{2}}$
$\frac{K_{2} l_{2} T_{1} + K_{1} l_{1} T_{2}}{K_{1} l_{1} + K_{2} l_{2}}$

Question

One end of a thermally insulated rod is kept at a temperature $T_{1}$ and the other at $T_{2}$ . The rod is composed of two sections of lengths $l_{1}$ and $l_{2}$ and thermal conductivities $K_{1}$ and $K_{2}$ respectively. The temperature at the interface of two sections is :

$\frac{K_{1} l_{2} T_{1} + K_{2} l_{1} T_{2}}{K_{1} l_{2} + K_{2} l_{1}}$
$\frac{K_{2} l_{1} T_{1} + K_{1} l_{2} T_{2}}{K_{2} l_{1} + K_{1} l_{2}}$
$\frac{K_{1} l_{1} T_{1} + K_{2} l_{2} T_{2}}{K_{1} l_{1} + K_{2} l_{2}}$
$\frac{K_{2} l_{2} T_{1} + K_{1} l_{1} T_{2}}{K_{1} l_{1} + K_{2} l_{2}}$

Toppr Admin · Accepted Answer

Let T be the temp at the interface-The rate of flow of heat remains same across the interface-The equation for heat flow in conduction is-dQdT-x2212-KAdTdx where- A is the cross section area across which heat flows-x21D2-K1A-T1-x2212-T-l1-K2A-T-x2212-T2-l2-x21D2-T1-x2212-T-l1K1-T-x2212-T2-l2K2-xA0-x21D2-T1-x2212-TT-x2212-T2-l1K2l2K1-x21D2-T-K1l2-K2l1-K1l2T1-K2l1T2-x21D2-T-K1l2T1-K2l1T2K1l2-K2l1