Three rods of identical cross-section and length are made of three different materials of thermal conductivity K 1 ,   K 2 and K 3 , respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100 ° C and the other at 0…

Question

Three rods of identical cross-section and length are made of three different materials of thermal conductivity $K_{1}, K_{2}$ and $K_{3}$ , respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at $100 ° C$ and the other at $0 ° C$ (see figure). If the joints of the rod are at $70 ° C$ and $20 ° C$ in steady and there is no loss of energy from the surface of the rod, the correct relationship between $K_{1}, K_{2}$ and $K_{3}$ is :

Aicharya · Accepted Answer

K 1 ( 100 - 70 ) = K 2 ( 70 - 20 ) = K 3 ( 20 - 0 ) K 1 30 = K 2 ( 50 ) = K 3 ( 20 ) &#8658; K 1 : K 2 : K 3 = 10 : 6 : 15 K 1 : K 3 = 2 : 3

Three rods of identical cross-section and length are made of three different materials of thermal…

Solution