The coefficient of thermal conductivity depends upon

Two bars of thermal conductivities $K$ and $3K$ and lengths $1\, cm$ and $2\, cm$ respectively have equal cross-sectional area. They are joined length-wise as shown in the figure. If the temperatures at the ends of this composite bar are $0\,^{\circ}C$ and $100\,^{\circ}C$ respectively,then the temperature $\varphi$ of the interface is......... $^oC$.

Three identical heat conducting rods are connected in series. The rods on the side have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state, temperature at the left junction is $T_1$ and that at the right junction is $T_2$. The ratio $T_1/T_2$ is

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ kept at temperatures $T_1$ and $T_2$,respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Two plates of equal area are placed in contact with each other. Their thicknesses are $2.0 \ cm$ and $5.0 \ cm$. The temperature of the outer surface of the first plate is $-20^{\circ}C$ and the temperature of the outer surface of the second plate is $20^{\circ}C$. If the ratio of their thermal conductivities is $2:5$,find the temperature of the contact surface in $^{\circ}C$.

$A$ metal cooking pot has a base area of $0.2 \,m^2$ and a thickness of $2.0 \,cm$. It boils water at a rate of $3.0 \,kg/min$ when placed on a hot plate. What is the temperature of the part of the hot plate in contact with the pot (in $^{\circ} C$)? [Thermal conductivity of metal is $120 \,J s^{-1} m^{-1} K^{-1}$, latent heat of vaporisation of water is $2 \times 10^6 \,J/kg$]