Three rods of equal length and cross-sectional area with thermal conductivities $K, 2K$,and $3K$ are joined as shown in the figure. The temperatures of their outer ends are $110\ ^oC, 20\ ^oC$,and $0\ ^oC$ respectively. Find the temperature of the junction in $^oC$.

$A$ rectangular ice box of total surface area of $1000 \,cm^2$ initially contains $1.5 \,kg$ of ice at $0^{\circ}C$. If the thickness of the walls of the box is $2 \,mm$ and the temperature outside the box is $42^{\circ}C$, then the mass of the ice remaining in the box after $160 \,minutes$ is (Thermal conductivity of the material of the box $= 10^{-2} \,W m^{-1} K^{-1}$ and latent heat of the fusion of ice $= 336 \times 10^3 \,J kg^{-1}$) (in $kg$)

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 $= 385 \; J s^{-1} m^{-1} K^{-1}$)

$A$ wall has two layers $A$ and $B$,each made of a different material. Both the layers have the same thickness. The thermal conductivity of the material of $A$ is twice that of $B$. Under thermal equilibrium,the temperature difference across the wall is $36\,^{\circ}C$. The temperature difference across the layer $A$ is ......... $^{\circ}C$

On a cold morning,a metal surface will feel colder to touch than a wooden surface because

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.