The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\  C$ and $210^o\ C$, the rate of heat flow will be…. $J/s$

A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of $0.1$ gm of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is $\frac{1}{4}$ that of first, the rate at which ice melts in $gm/\sec $will be

An insulated container is filled with ice at $0\,^oC$ , and another container is filled with water that is continuously boiling at $100\,^oC$ . In series of experiments, the containers are connected by various thick metal rods that pass through the walls of container as shown in the figure

In the experiment $I$ : a copper rod is used and all ice melts in $20$ minutes.

In the experiment $II$ : a steel rod of identical dimensions is used and all ice melts in $80$ minutes.

In the experiment $III$ : both the rods are used in series and all ice melts in $t_{10}$ minutes.

In the experiment $IV$ : both rods are used in parallel and all ice melts in $t_{20}$ minutes.

Give definition, unit and dimensional formula of thermal conductivity.

A partition wall has two layers $A$ and $B$ in contact, each made of a different material. They have the same thickness but the thermal conductivity of layer $A$ is twice that of layer $B$. If the steady state temperature difference across the wall is $60K$, then the corresponding difference across the layer $A$ is ……. $K$