Four rods of same material and having the same cross section and length have been joined, as shown. The temperature of the junction of four rods will be ............... $^{\circ} C$

A composite metal bar of uniform section is made up of length $25 cm$ of copper, $10  cm$ of nickel and $15 cm$ of aluminium. Each part being in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at ${100^o}C$ and the aluminium end at ${0^o}C$. The whole rod is covered with belt so that there is no heat loss occurs at the sides. If ${K_{{\rm{Cu}}}} = 2{K_{Al}}$ and ${K_{Al}} = 3{K_{{\rm{Ni}}}}$, then what will be the temperatures of $Cu - Ni$ and $Ni - Al$ junctions respectively

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $30$ minutes. The ratio of their thermal conductivities will be

When two ends of a rod wrapped with cotton are maintained at different temperatures and after some time every point of the rod attains a constant temperature, then

A large cylindrical rod of length $L$ is made by joining two identical rods of copper and steel of length $(\frac {L}{2})$ each . The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at $100\,^oC$ and that of steel at $0\,^oC$ then the temperature of junction is........$^oC$ (Thermal conductivity of copper is $9\,times$ that of steel)

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ , respectively are $T_2$ and $T_1$ ($T_2$ > $T_1$). The rate of heat transfer through the slab, in a steady state is $\left( {\frac{{A({T_2} - {T_1})K}}{x}} \right)f$, with $f $ which equal to