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....... $^{\circ}C$

Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle $ABC$,right-angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt{2}T$ respectively. In the steady state,the temperature of point $C$ is $T_C$. Assuming that only heat conduction takes place,$\frac{T_C}{T}$ is equal to

Dimensional formula for thermal conductivity is (here $K$ denotes the temperature)

On which factor does the thermal conductivity depend?

Two thin metallic spherical shells of radii $r_{1}$ and $r_{2}$ $(r_{1} < r_{2})$ are placed with their centres coinciding. $A$ material of thermal conductivity $K$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}$ $(\theta_{1} < \theta_{2})$. The rate at which heat flows radially through the material is:

$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \ cal/sec$. If all the linear dimensions are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be: