Three rods of same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown in the figure. In the steady state,the temperature of the junction $P$ is:

Two metal rods $1$ and $2$ have the same length and the same temperature difference at their ends. Their thermal conductivities are $K_1$ and $K_2$ and their cross-sectional areas are $A_1$ and $A_2$ respectively. The condition for the same rate of heat flow in them is ........

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1=300 \ K$ and $T_2=100 \ K$,as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K_1$ and $K_2$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200 \ K$,then $K_1 / K_2 = . . . . . .$

The ends of two rods of different materials with their thermal conductivities,radii of cross-sections,and lengths all in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4 \; cal/sec$,the rate of flow of heat in the shorter rod in $cal/sec$ will be:

The heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,the ratio of the rate of flow of heat through them will be:

On heating one end of a rod,the temperature of the whole rod will be uniform when