$ABCDE$ is a regular pentagon of uniform wire. The rate of heat entering at $A$ and leaving at $C$ is equal. $T_B$ and $T_D$ are temperature of $B$ and $D$ . Find the temperature $T_C$

Three rods of same material, same area of crosssection but different lengths $10 \,cm , 20 \,cm$ and $30 \,cm$ are connected at a point as shown. What is temperature of junction $O$ is ......... $^{\circ} C$

he ratio of the coefficient of thermal conductivity of two different materials is $5 : 3$ . If the thermal resistance of the rod and thickness of these materials is same, then the ratio of the length of these rods will be

Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state, if the temperatures at the outer surfaces are ${T_1}$ and ${T_2}$, the temperature at the common wall is

A wall consists of alternating blocks of length $d$ and coefficient of thermal conductivity $K_{1}$ and $K_{2}$ respectively as shown in figure. The cross sectional area of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between left and right is

A brass boiler has a base area of $0.15\; m ^{2}$ and thickness $1.0\; cm .$ It boils water at the rate of $6.0\; kg / min$ when placed on a gas stove. Estimate the temperature (in $^oC$) of the part of the flame in contact with the boiler. Thermal conductivity of brass $=109 \;J s ^{-1} m ^{-1} K ^{-1} ;$ Heat of vaporisation of water $=2256 \times 10^{3}\; J kg ^{-1}$