The two ends of a rod of length $x$ and uniform cross-sectional area $A$ are kept at temperatures $T_1$ and $T_2$ respectively $(T_1 > T_2)$. If the rate of heat transfer through the rod in steady state is $Q/t$,then the coefficient of thermal conductivity $K$ is:

Rate of flow of heat through a cylindrical rod is $H_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod become double and the temperature difference remains the same, and if the rate of flow of heat becomes $H_2$, then $H_2 =$

The outer faces of a rectangular slab made of equal thickness of iron and brass are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The temperature at the interface is ........... $^{\circ} C$ (Thermal conductivity of iron and brass are $0.2$ and $0.3$ respectively.)

One end of a metal rod of length $1.0 \ m$ and area of cross-section $100 \ cm^2$ is maintained at $100^{\circ}C$. If the other end of the rod is maintained at $0^{\circ}C$,the quantity of heat transmitted through the rod per minute is (Coefficient of thermal conductivity of the material of the rod = $100 \ W/m-K$).

Two identical containers are filled with the same amount of ice. The containers are made of different metals. If the ice in both containers melts in $20$ minutes and $35$ minutes respectively,find the ratio of their thermal conductivities.

Two thin metallic spherical shells of radii $20 \text{ cm}$ and $30 \text{ cm}$, respectively, are placed with their centers coinciding. $A$ material of thermal conductivity $\alpha$ is filled in the space between the shells. The inner shell is maintained at $300 \text{ K}$ and the outer shell at $310 \text{ K}$. If the rate at which heat flows radially through the material is $40 \text{ W}$, find the value of $\alpha$ (in units of $\text{J s}^{-1} \text{ m}^{-1} \text{ K}^{-1}$).