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
$K _{1}: K _{3}=2: 3 ; K _{2}: K _{3}=2: 5$
$K _{1}< K _{2}< K _{3}$
$K _{1}: K _{2}=5: 2 ; K _{1}: K _{3}=3: 5$
$K _{1}> K _{2}> K _{3}$
On heating one end of a rod, the temperature of whole rod will be uniform when
For the shown figure, calculate the equivalent thermal resistance if the bricks made of the same material of conductivity $K$
Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities $ K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is
Three rods $A, B$ and $C$ of thermal conductivities $K, 2\,K$ and $4\,K$, cross-sectional areas $A, 2\,A$ and $2\,A$ and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100^o\,C, 50^o\,C$, and $0^o\,C$ respectively, then the temperature $\theta$ of the junction is ......... $^oC$
A hollow sphere of inner radius $R$ and outer radius $2R$ is made of a material of thermal conductivity $K$. It is surrounded by another hollow sphere of inner radius $2R$ and outer radius $3R$ made of same material of thermal conductivity $K$. The inside of smaller sphere is maintained at $0^o C$ and the outside of bigger sphere at $100^o C$. The system is in steady state. The temperature of the interface will be ........ $^oC$