Three rods of identical cross-section and lengths 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 $100^{\circ} C$ and the ther at $0^{\circ} C$ (see figure). If the joints of the rod are at  $70^{\circ} C$ and $20^{\circ} C$ in steady state 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 

981-202

  • [JEE MAIN 2020]
  • A

    $K _{1}: K _{3}=2: 3 ; K _{2}: K _{3}=2: 5$

  • B

    $K _{1}< K _{2}< K _{3}$

  • C

    $K _{1}: K _{2}=5: 2 ; K _{1}: K _{3}=3: 5$

  • D

    $K _{1}> K _{2}> K _{3}$

Similar Questions

The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in the figure. What will be the temperature at the junction of copper and steel ....... $^oC$

Four rods of same material and having the same cross section and length have been joined, as shown. The temperature of the junction of four rods will be ............... $^{\circ} C$

Three identical rods have been joined at a junction to make it a $Y$ shape structure. If two free ends are maintained at $90\,^oC$ and the third end is at $30\,^oC$ , then what is the junction temperature $\theta $ ?......... $^oC$

Two rods $A$ and $B$ of same cross-sectional are $A$ and length $l$ connected in series between a source $(T_1 = 100^o C)$ and a sink $(T_2 = 0^o C)$ as shown in figure. The rod is laterally insulated  If $G_A$ and $G_B$ are the temperature gradients across the rod $A$ and $B$, then 

The heat is flowing through a rod of length $50 cm$ and area of cross-section $5c{m^2}$. Its ends are respectively at ${25^o}C$ and ${125^o}C$. The coefficient of thermal conductivity of the material of the rod is $0.092 kcal/m×s×^\circ C$. The temperature gradient in the rod is