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

Two plates of equal area are placed in series. The ratios of their thicknesses and thermal conductivities are both $2:3$. The temperature of the outer surface of one plate is $100 ^\circ C$ and that of the other is $0 ^\circ C$. The temperature of the common surface is ....... $^\circ C$.

$A$ metal rod $AB$ of length $10x$ has its one end $A$ in ice at $0^{\circ}C$ and the other end $B$ in water at $100^{\circ}C$. If a point $P$ on the rod is maintained at $400^{\circ}C$,then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is $540 \ cal/g$ and latent heat of melting of ice is $80 \ cal/g$. If the point $P$ is at a distance of $\lambda x$ from the ice end $A$,find the value of $\lambda$. (Neglect any heat loss to the surrounding.)

$1.56 \times 10^5 \ J$ of heat is conducted through a $2 \ m^2$ wall of $12 \ cm$ thickness in one hour. The temperature difference between the two sides of the wall is $20^{\circ} C$. The thermal conductivity of the material of the wall is (in $W \ m^{-1} \ K^{-1}$):

Two metal rods $P$ and $Q$ have the same length and the same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$,and their cross-sectional areas are $A_1$ and $A_2$ respectively. If the rate of flow of heat through rod $Q$ is three times that in rod $P$,then:

The ends of two rods of different materials with their thermal conductivities,radii of cross-sections,and lengths all in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4 \; cal/sec$,the rate of flow of heat in the shorter rod in $cal/sec$ will be: