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

Four rods of the same material and having the same cross-section and length have been joined as shown in the figure. The temperature of the junction of the four rods will be ............... $^{\circ}C$.

The rate of flow of heat through a copper rod with a temperature difference of $28^{\circ} C$ is $1400 \ cal s^{-1}$. The thermal resistance of the copper rod will be:

Two rods whose lengths are $l_1$ and $l_2$ with thermal conductivity coefficients $k_1$ and $k_2$ are placed end to end. The thermal conductivity coefficient of a uniform rod of length $l_1+l_2$ whose thermal resistance is the same as that of the system of these two rods is

$A$ copper rod $2 \ m$ long has a circular cross-section of radius $1 \ cm$. One end is kept at $100^{\circ}C$ and the other at $0^{\circ}C$,and the surface is covered by non-conducting material to prevent heat losses through the surface. The thermal resistance of the bar in Kelvin per Watt is (Take thermal conductivity $K = 401 \ W/m-K$ of copper):- (in $.9$)

Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $k_1$ and $k_2$ respectively. $A$ steady temperature difference of $12^{\circ} C$ is maintained across the composite slab. If $k_1=\frac{k_2}{2}$, the temperature difference across slab $A$ is (in $^{\circ} C$)