A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$

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 

In the Ingen Hauz’s experiment the wax melts up to lengths $10$ and $25 cm$ on two identical rods of different materials. The ratio of thermal conductivities of the two materials is

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

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at ${0^o}C$ and ${90^o}C$ respectively. The temperature of the junction of the three rods will be ...... $^oC$

A rod of length $L$ and uniform cross-sectional area has varying thermal conductivity which changes linearly from $2K$ at endAto $K$ at the other end $B$. The endsA and $B$ of the rod are maintained at constant temperature $100^o C$ and $0^o C$, respectively. At steady state, the graph of temperature : $T = T(x)$ where $x =$ distance from end $A$ will be