On a cold morning,a metal surface will feel colder to touch than a wooden surface because

Two spheres made of different materials have radii in the ratio $2:1$ and wall thicknesses in the ratio $1:4$. They are completely filled with ice. If the time taken to melt the ice completely in the larger sphere is $25 \ min$ and in the smaller sphere is $16 \ min$,then the ratio of the thermal conductivities of the materials of the larger and smaller spheres is ..........

The temperature difference between two sides of an iron plate,$1.8 \ cm$ thick is $9^{\circ} C$. Heat is transmitted through the plate at a rate of $10 \ kcal / (s \cdot m^2)$ at steady state. The thermal conductivity of iron is:

Two metallic blocks $M_{1}$ and $M_{2}$ of the same cross-sectional area are connected to each other as shown in the figure. If the thermal conductivity of $M_{2}$ is $K$,then the thermal conductivity of $M_{1}$ will be $xK$. Find the value of $x$. [Assume steady-state heat conduction]

If $K_{1}$ and $K_{2}$ are the thermal conductivities,$L_{1}$ and $L_{2}$ are the lengths,and $A_{1}$ and $A_{2}$ are the cross-sectional areas of steel and copper rods respectively,such that $\frac{K_{2}}{K_{1}}=9$,$\frac{A_{1}}{A_{2}}=2$,and $\frac{L_{1}}{L_{2}}=2$. For the arrangement shown in the figure,the value of the temperature $T$ of the steel-copper junction in the steady state will be ........... $^{\circ}C$.

Wires $A$ and $B$ have identical lengths and have circular cross-sections. The radius of $A$ is twice the radius of $B$,$i.e.$,${r_A} = 2{r_B}$. For a given temperature difference between the two ends,both wires conduct heat at the same rate. The relation between the thermal conductivities is given by: