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,the rate of flow of heat becomes $H_2$. Then:

The coefficient of thermal conductivity of a rod depends on its

Two identical long bars $A$ and $B$ made of different materials are coated with wax and have one end immersed in a hot oil bath. When the steady state is reached, the lengths for which the wax melts are $l_A$ and $l_B$. If $k_A$ and $k_B$ are the thermal conductivities of the materials, then:

Two plates of equal area are placed in series. The ratios of their thicknesses and thermal conductivities are both $2:3$. The temperature of the outer surface of one plate is $100 ^\circ C$ and that of the other is $0 ^\circ C$. The temperature of the common surface is ....... $^\circ C$.

Two metal cubes $A$ and $B$ of the same size are arranged as shown in the figure. The ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. If the thermal conductivities of $A$ and $B$ are $300 \, W/m \, ^\circ C$ and $200 \, W/m \, ^\circ C$ respectively,find the temperature $t$ at the junction when the steady state is reached.

Two rods have thermal conductivities $K$ and $3K$ and lengths $1 \ cm$ and $2 \ cm$ respectively. Their cross-sectional areas are equal. They are joined in series as shown in the figure. If the temperatures of the outer ends of this composite rod are $0^{\circ}C$ and $100^{\circ}C$ respectively,find the junction temperature $\phi$ in $^{\circ}C$.