Two rods having thermal conductivity in the ratio of $5 : 3$ having equal lengths and equal cross-sectional area are joined by face to face. If the temperature of the free end of the first rod is $100°C$ and free end of the second rod is $20°C$ . Then temperature of the junction is…… $^oC$

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at ${0^o}C$ and ${90^o}C$ respectively. The temperature of the junction of the three rods will be …… $^oC$

The end $A$ of a rod $AB$ of length $1\,m$ is maintained at $80\,^oC$ and the end $B$ at $0\,^oC.$ The temperature at a distance of  $60\,\,c.m.$  from the end $A$  is……… $^oC$

There are two identical vessels filled with equal amounts of ice. The vessels are of different metals., If the ice melts in the two vessels in $20$ and $35$ minutes respectively, the ratio of the coefficients of thermal conductivity of the two metals is

Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state, if the temperatures at the outer surfaces are ${T_1}$ and ${T_2}$, the temperature at the common wall is