$A$ 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:

In Searle's method for finding the thermal conductivity of metals,the temperature gradient along the bar:

The thermal conductivity of copper is $9$ times that of steel. Find the temperature of the junction of copper and steel in the composite rod as shown in the figure (in $^oC$).

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state,the temperature at the left junction is $T_1$ and that at the right junction is $T_2$. The ratio $T_1 / T_2$ is

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

There is a layer of snow $x \ cm$ thick on water,when the temperature of the air is $-\theta ^\circ C$ (less than the freezing point). If the thickness of the layer increases from $x$ to $y$ in time $t$,then the value of $t$ is given by: