Two spheres of different materials,one with double the radius and one-fourth wall thickness of the other,are filled with ice. If the time taken for complete melting of ice in the large radius sphere is $25 \ minutes$ and that for the smaller one is $16 \ minutes$,the ratio of thermal conductivities of the materials of the larger sphere to the smaller sphere is:

Two rods with thermal conductivities $K$ and $3K$ and equal cross-sectional areas are joined as shown in the figure. Their lengths are $1 \ cm$ and $2 \ cm$,respectively. If the temperatures of the two ends of this composite rod are $0^{\circ}C$ and $100^{\circ}C$ (see figure),then the temperature $\phi$ of their interface is:

Two spheres made of different materials have radii in the ratio $2:1$ and wall thicknesses in the ratio $1:4$. They are completely filled with ice. If the time taken to melt the ice completely in the larger sphere is $25 \ min$ and in the smaller sphere is $16 \ min$,then the ratio of the thermal conductivities of the materials of the larger and smaller spheres is ..........

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:

Two rods have thermal conductivities $K$ and $3K$ and lengths $1 \ cm$ and $2 \ cm$ respectively. Their cross-sectional areas are equal. They are joined in series as shown in the figure. If the temperatures of the outer ends of this composite rod are $0^{\circ}C$ and $100^{\circ}C$ respectively,find the junction temperature $\phi$ in $^{\circ}C$.

On a cold morning,a metal surface feels colder than a wooden surface because: