On a winter morning,a metal surface feels colder to the touch than a wooden surface because:

Two walls of thickness $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state,the temperatures of the outer surfaces are $T_1$ and $T_2$. Find the temperature of the common interface.

The thermal conductivity of a material in $CGS$ system is $0.4$. In steady state,the rate of flow of heat is $10 \ cal/sec-cm^2$. Then the thermal gradient will be ....... $^oC/cm$.

One end of a copper rod of length $1.0 \; m$ and area of cross-section $10^{-3} \; m^2$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $92 \; cal/(m \cdot s \cdot ^\circ C)$ and the latent heat of ice is $8 \times 10^4 \; cal/kg$,then the amount of ice which will melt in one minute is:

The temperature difference between the ends of two cylindrical rods $A$ and $B$ of the same material is $2: 3$. In steady state,the ratio of the rates of flow of heat through the rods $A$ and $B$ is $5: 9$. If the radii of the rods $A$ and $B$ are in the ratio $1: 2$,then the ratio of lengths of the rods $A$ and $B$ is

$A$ brass rod of length $2 \ m$ and radius $1 \ cm$ has one end maintained at $250 \ ^oC$. When steady state is reached, the rate of heat flow through any cross-section is $0.5 \ cal \ s^{-1}$. Find the temperature of the other end in $^oC$. (Thermal conductivity of brass $K = 0.26 \text{ cal s}^{-1} \text{ cm}^{-1} \text{ } ^\circ\text{C}^{-1}$)