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 temperatures of the two outer surfaces of a composite slab,consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thicknesses $x$ and $4x$ respectively,are $T_2$ and $T_1$ $(T_2 > T_1)$. The rate of heat transfer through the slab in a steady state is $\left( \frac{A(T_2 - T_1)K}{x} \right)f$,where $f$ is equal to:

Two rectangular blocks,having identical dimensions,can be arranged either in configuration $I$ or in configuration $II$ as shown in the figure. One of the blocks has thermal conductivity $k$ and the other $2k$. The temperature difference between the ends along the $x$-axis is the same in both the configurations. It takes $9 \ s$ to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is: (in $s$)

$A$ copper rod of length $18 \ cm$ and a steel rod of length $6 \ cm$ are joined together to form a composite rod of uniform cross-section. The temperature of the free end of the copper rod is $100 \ ^\circ C$ and the temperature of the free end of the steel rod is $0 \ ^\circ C$. What is the temperature at the junction in $^\circ C$? (Thermal conductivity of copper is $9$ times that of steel. The rod is in a steady state.)

Two identical conducting rods are first connected independently in parallel to two vessels,one containing water at $100^oC$ and the other containing ice at $0^oC$. In the second case,the rods are joined end to end (in series) and connected to the same vessels. Let $q_1$ and $q_2$ $g/s$ be the rate of melting of ice in the two cases respectively. The ratio of $q_1/q_2$ is

Two rods of cross-sectional area $A$ and $2A$ and equal length having thermal conductivities $2K$ and $3K$ are joined in parallel. The equivalent thermal conductivity of their combination will be: