Four identical rods of the same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is $100^{\circ}C$,then the temperature difference between the ends of the other diagonal will be ........ $^{\circ}C$.

Two plates of the same thickness with coefficients of thermal conductivities $K_1$ and $K_2$ and cross-sectional areas $A_1$ and $A_2$ are connected as shown. Find the effective coefficient of thermal conductivity $K_{eq}$.

$A$ cylinder of thermal conductivity $k_1$ and radius $r$ is surrounded by a cylindrical shell of inner radius $r$,outer radius $2r$,and thermal conductivity $k_2$. Both cylinders have the same length and the temperature difference across their ends is the same. The equivalent thermal conductivity of the system is:

In the following figure,two insulating sheets with thermal resistances $R$ and $3R$ are shown. The temperature $\theta$ at the interface is ...... $^oC$.

$A$ copper rod $2 \ m$ long has a circular cross-section of radius $1 \ cm$. One end is kept at $100^{\circ}C$ and the other at $0^{\circ}C$,and the surface is covered by non-conducting material to prevent heat losses through the surface. The thermal resistance of the bar in Kelvin per Watt is (Take thermal conductivity $K = 401 \ W/m-K$ of copper):- (in $.9$)

Two cylinders $P$ and $Q$ have the same length and diameter and are made of different materials having thermal conductivities in the ratio $2 : 3$. These two cylinders are combined to make a single cylinder. One end of $P$ is kept at $100^{\circ}C$ and the other end of $Q$ is kept at $0^{\circ}C$. The temperature at the interface of $P$ and $Q$ is ...... $^{\circ}C$.