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

Two metal rods $1$ and $2$ have the same length and the same temperature difference at their ends. Their thermal conductivities are $K_1$ and $K_2$ and their cross-sectional areas are $A_1$ and $A_2$ respectively. The condition for the same rate of heat flow in them is ........

Define thermal conductivity. Also,provide its $SI$ unit and dimensional formula.

Why does a metal bar appear hotter than a wooden bar at the same temperature? Equivalently,it also appears cooler than a wooden bar if they are both colder than room temperature.

Two rectangular blocks $A$ and $B$ of different metals have the same length and the same area of cross-section. They are kept in such a way that their cross-sectional areas touch each other. The temperature at one end of $A$ is $100^{\circ}C$ and that of $B$ at the other end is $0^{\circ}C$. If the ratio of their thermal conductivities is $1 : 3$,then under steady state,the temperature of the junction in contact will be ........ $^{\circ}C$.

Three conducting rods of the same material and cross-section are shown in the figure. The temperatures of $A$,$D$,and $C$ are maintained at $20^{\circ} C$,$90^{\circ} C$,and $0^{\circ} C$ respectively. If there is no heat flow in rod $AB$,the ratio of the lengths of $BD$ and $BC$ is: