In an $Ingen-Hauz$ experiment,the wax melts on two rods up to lengths of $10 \ cm$ and $25 \ cm$ respectively. If the two rods are made of different materials,what is the ratio of their thermal conductivities?

$A$ cylindrical steel rod of length $0.10 \,m$ and thermal conductivity $50 \,Wm^{-1}K^{-1}$ is welded end to end to a copper rod of thermal conductivity $400 \,Wm^{-1}K^{-1}$ and of the same area of cross-section but $0.20 \,m$ long. The free end of the steel rod is maintained at $100^{\circ}C$ and that of the copper rod at $0^{\circ}C$. Assuming that the rods are perfectly insulated from the surroundings,the temperature at the junction of the two rods is ................... $^{\circ}C$.

$A$ conducting rod of length $1 \,m$ has an area of cross-section $10^{-3} \,m^2$. One end is immersed in boiling water $(100^{\circ} C)$ and the other end in ice $(0^{\circ} C)$. If the coefficient of thermal conductivity of the rod is $96 \,cal/(s \cdot m \cdot ^{\circ}C)$ and the latent heat of fusion for ice is $8 \times 10^4 \,cal/kg$,then the amount of ice that will melt in one minute is:

The coefficient of thermal conductivity of a metal rod depends on its

The thermal conductivity of a material in $CGS$ system is $0.4$. In steady state,the rate of flow of heat is $10 \ cal/sec-cm^2$. Then the thermal gradient will be ....... $^oC/cm$.

These days,people use steel utensils with copper bottoms. This is considered good for uniform heating of food. Explain this effect using the fact that copper is a better conductor of heat.