Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$, respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are  $\theta_2$ and $\theta_1$ respectively  $\left( {\theta _2} > {\theta _1} \right)$ . The temperature at the interface is

For the figure shown, when arc $ACD$ and $ADB$ are made of same material, the heat carried between $A$ and $B$ is $H$ . If $ADB$ is replaced with another material, the heat carried becomes $2H$ . If the temperatures at $A$ and $B$ are fixed at $T_1$ and $T_2$ , what is the ratio of the new conductivity to the old one of $ADB$

The only possibility of heat flow in a thermos flask is through its cork which is $75 cm^2$ in area and $5 cm$ thick. Its thermal conductivity is $0.0075 cal/cmsec^oC$. The outside temperature is$ 40^oC$ and latent heat of ice is $80 cal g^{-1}$. Time taken by $500 g$ of ice at $0^oC$ in the flask to melt into water at $0^oC$ is ……. $hr$

Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is ${100^o}C$, then the temperature difference between the ends of other diagonal will be …….. $^oC$