The thermal conductivities of copper,mercury,and glass are $K_c$,$K_m$,and $K_g$ respectively,such that $K_c > K_m > K_g$. If the same amount of heat flows per unit time through a unit cross-sectional area for each,what is the relationship between their temperature gradients $(X_c, X_m, X_g)$?

In a steady state,the temperatures at the ends $A$ and $B$ of a $20\,cm$ long rod $AB$ are $100\,^{\circ}C$ and $0\,^{\circ}C$ respectively. The temperature of a point $C$ at a distance of $9\,cm$ from $A$ is....... $^{\circ}C$

Four identical conducting rods are joined to form a square $ABCD$. The temperatures of junctions $A, B,$ and $C$ are maintained at $100^{\circ}C, 40^{\circ}C,$ and $0^{\circ}C$ respectively. Choose the $\text{INCORRECT}$ statement for this arrangement in a steady state. (The value of $\frac{KA}{L} = 1 \text{ J}/(s \cdot ^{\circ}C)$).

An ice box used for keeping eatables cold has a total wall area of $1\;m^2$ and a wall thickness of $5.0\;cm$. The thermal conductivity of the ice box material is $K = 0.01\;J/(m\cdot s\cdot ^\circ C)$. It is filled with ice at $0^\circ C$ along with eatables on a day when the temperature is $30^\circ C$. The latent heat of fusion of ice is $334 \times 10^3\;J/kg$. The amount of ice melted in one day is ........ $g$ $(1\;day = 86,400\;s)$.

If the radius and length of a copper rod are both doubled,the rate of flow of heat along the rod increases ....... times.

The coefficient of thermal conductivity of a rod depends on its