$A$ wall is made of two layers of thickness $1\ cm$ and $4\ cm$ and thermal conductivities $K$ and $3K$ respectively. If the temperature difference across the wall is $50\ ^oC$,then the temperature difference across the thin layer will be

The ratio of the coefficient of thermal conductivity of two different materials is $5 : 3$. If the thermal resistance of the rods and the cross-sectional area of these materials are the same,then the ratio of the lengths of these rods will be

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 $0^{\circ}C$ and $90^{\circ}C$ respectively. The temperature of the junction of the three rods will be ...... $^{\circ}C$.

$A$ composite metal bar of uniform cross-section is made up of a length of $25 \ cm$ of copper,$10 \ cm$ of nickel,and $15 \ cm$ of aluminium. Each part is in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at $100^{\circ}C$ and the aluminium end at $0^{\circ}C$. The whole rod is covered with an insulating belt so that no heat loss occurs at the sides. If $K_{\text{Cu}} = 2K_{\text{Al}}$ and $K_{\text{Al}} = 3K_{\text{Ni}}$,what will be the temperatures of the $\text{Cu-Ni}$ and $\text{Ni-Al}$ junctions,respectively?

$A$ hollow sphere of inner radius $R$ and outer radius $2R$ is made of a material of thermal conductivity $K$. It is surrounded by another hollow sphere of inner radius $2R$ and outer radius $3R$ made of the same material of thermal conductivity $K$. The inside of the smaller sphere is maintained at $0^oC$ and the outside of the bigger sphere at $100^oC$. The system is in steady state. The temperature of the interface will be ........ $^oC$.

$A$,$B$ and $C$ are three identical conductors but made from different materials. They are kept in contact as shown. Their thermal conductivities are $K$,$2K$ and $K/2$. The free end of $A$ is at $100^{\circ} C$ and the free end of $C$ is at $0^{\circ} C$. During steady state,the temperature of the junction of $A$ and $B$ is nearly (in $^{\circ} C$)