$A$ cylindrical rod has temperatures $\theta_1$ and $\theta_2$ at its ends. The rate of heat flow is $Q \ J s^{-1}$. All the linear dimensions of the rod are doubled while keeping the temperatures constant. What is the new rate of flow of heat?

Which of the following material is most suitable for cooking utensils?

For a spherical shell with inner and outer radii $r_1$ and $r_2$ respectively,the formula for the heat flow rate is = ......... where $T_1$ and $T_2$ are the temperatures of the inner and outer surfaces of the shell $(T_1 > T_2)$. The thermal conductivity of the material of the shell is $k$.

The ratio of the thermal conductivity of two rods of different materials is $6:5$. The two rods of same area of cross section and same thermal resistance will have the lengths in the ratio:

What is the temperature (in $^oC$) of the steel-copper junction in the steady state of the system shown in the figure? Length of the steel rod $= 15.0 \; cm,$ length of the copper rod $= 10.0 \; cm,$ temperature of the furnace $= 300^{\circ} C,$ temperature of the other end $= 0^{\circ} C.$ The area of cross-section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel $= 50.2 \; J s^{-1} m^{-1} K^{-1};$ and of copper $= 385 \; J s^{-1} m^{-1} K^{-1}$)

Two slabs have thicknesses $d_{1}$ and $d_{2}$. Their thermal conductivities are $K_{1}$ and $K_{2}$ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures $\theta_{1}$ and $\theta_{2}$. Assume $\theta_{1} > \theta_{2}$. The temperature $\theta$ of their common junction is