$A$ metal rod of length $2\, m$ has cross-sectional areas $2A$ and $A$ as shown in the figure. The two ends are maintained at temperatures $100\,^{\circ}C$ and $70\,^{\circ}C$. The temperature of the junction point $C$ is ........ $^{\circ}C$.

$A$ cylindrical copper rod of length $2 \,m$ and cross-sectional area $2 \,cm^2$ is insulated at its curved surface. One end of the rod is maintained in a steam chamber at $100^{\circ} C$ and the other is maintained in ice at $0^{\circ} C$. The thermal conductivity of copper is $386 \,Js^{-1} \,m^{-1} {}^{\circ} C^{-1}$. Find the temperature at a point which is at a distance of $120 \,cm$ from the colder end. (in $^{\circ} C$)

Two rods $A$ and $B$ of the same cross-sectional area $A$ and length $l$ are connected in series between a source $(T_1 = 100^{\circ}C)$ and a sink $(T_2 = 0^{\circ}C)$ as shown in the figure. The rods are laterally insulated. If the thermal conductivities of rods $A$ and $B$ are $3K$ and $K$ respectively,and $T_A$ and $T_B$ are the temperature drops across rods $A$ and $B$,then:

One end of a copper rod of length $1.0 \; m$ and area of cross-section $10^{-3} \; m^2$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $92 \; cal/(m \cdot s \cdot ^\circ C)$ and the latent heat of ice is $8 \times 10^4 \; cal/kg$,then the amount of ice which will melt in one minute is:

Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities $K_1, K_2, K_3, K_4$ and $K_5$. When points $A$ and $B$ are maintained at different temperatures,no heat flows through the central rod if

In which case does the thermal conductivity increase from left to right?