If the ratio of coefficient of thermal conductivity of silver and copper is $10 : 9$ , then the ratio of the lengths upto which wax will melt in Ingen Hausz experiment will be

hree rods of same dimensions are arranged as shown in figure they have thermal conductivities ${K_1},{K_2}$ and${K_3}$ The points $P$ and $Q$ are maintained at different temperatures for the heat to flow at the same rate along $PRQ$ and $PQ$ then which of the following option is correct

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $K _{1}, K _{2},$ and $K _{3}$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at $100^{\circ} C$ and the ther at $0^{\circ} C$ (see figure). If the joints of the rod are at  $70^{\circ} C$ and $20^{\circ} C$ in steady state and there is no loss of energy from the surface of the rod, the correct relationship between $K _{1}, K _{2}$ and $K _{3}$ is 

What is the temperature (in $^oC$) of the steel-copper junction in the steady state of the system shown in Figure Length of the steel rod $=15.0\; cm ,$ length of the copper rod $=10.0\; cm ,$ temperature of the furnace $=300^{\circ} C ,$ temperature of the other end $=0^{\circ} C .$ The area of cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel $=50.2 \;J s ^{-1} m ^{-1} K ^{-1} ;$ and of copper $\left.=385 \;J s ^{-1} m ^{-1} K ^{-1}\right)$

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ 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 $\left( {\frac{{A({T_2} – {T_1})K}}{x}} \right)f$, with $f $ which equal to