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.

Two thin blankets keep more hotness than one blanket of thickness equal to these two. The reason is

A composite rod made of three rods of equal length and cross-section as shown in the fig. The thermal conductivities of the materials of the rods are $K/2, 5K$ and $K$ respectively. The end $A$ and end $B$ are at constant temperatures. All heat entering the face Agoes out of the end $B$ there being no loss of heat from the sides of the bar. The effective thermal conductivity of the bar is

A thin paper cup filled with water does not catch fire when placed over a flame. This is because

The two opposite faces of a cubical piece of iron (thermal conductivity $= 0.2\, CGS$ units) are at ${100^o}C$ and ${0^o}C$ in ice. If the area of a surface is $4c{m^2}$, then the mass of ice melted in $10$ minutes will be ...... $gm$

The ratio of thermal conductivity of two rods of different material is $5 : 4$ . The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio