Two identical metal wires of thermal conductivities $K_{1}$ and $K_{2}$ respectively are connected in series. The effective thermal conductivity of the combination is

In a composite rod,when two rods of different lengths $l_1$ and $l_2$ and of the same cross-sectional area are joined end to end,if $K$ is the effective coefficient of thermal conductivity,then the value of $(l_1 + l_2)/K$ is

Three rods $AB, BC$ and $AC$ having thermal resistances of $10 \text{ units}, 10 \text{ units}$ and $20 \text{ units}$ respectively,are connected as shown in the figure. Ends $A$ and $C$ are maintained at constant temperatures of $100^{\circ}C$ and $0^{\circ}C$ respectively. The rate at which the heat is crossing junction $B$ is . . . . . . $units$.

Two walls have thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$,respectively. In the steady state,the temperatures of the outer surfaces are $T_1$ and $T_2$. What is the temperature at the interface of the two walls?

The ratio of thermal conductivities of two materials is $1 : 2$. If the ratio of the lengths of the rods of these materials is $1 : 2$ and the ratio of their cross-sectional areas is $2 : 1$,then the ratio of their thermal resistances is:

Three conductors of the same length having thermal conductivities $k_1, k_2$ and $k_3$ are connected as shown in the figure. The areas of cross-section of the $1^{\text{st}}$ and $2^{\text{nd}}$ conductors are the same,and for the $3^{\text{rd}}$ conductor,it is double that of the $1^{\text{st}}$ conductor. The temperatures are given in the figure. In the steady-state condition,the value of $\theta$ is . . . . . . $^{\circ}C$. (Given: $k_1 = 60 \ J s^{-1} m^{-1} K^{-1}, k_2 = 120 \ J s^{-1} m^{-1} K^{-1}, k_3 = 135 \ J s^{-1} m^{-1} K^{-1}$)