If two metallic plates of equal thicknesses and thermal conductivities ${K_1}$ and ${K_2}$ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

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 ice in the large radius one is $25$ minutes and that for smaller one is $16$ minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is

Three rods of same material, same area of crosssection but different lengths $10 \,cm , 20 \,cm$ and $30 \,cm$ are connected at a point as shown. What is temperature of junction $O$ is ……… $^{\circ} C$

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ , respectively are $T_2$ and $T_1$ ($T_2$ > $T_1$). The rate of heat transfer through the slab, in a steady state is $\left( {\frac{{A({T_2} – {T_1})K}}{x}} \right)f$, with $f $ which equal to

Two bars of thermal conductivities $K$ and $3K$ and lengths $1\,\, cm$ and $2\,\, cm$ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $0\,^oC$ and $100\,^oC$ respectively (see figure), then the temperature $\varphi $ of the interface is……… $^oC$