Two identical containers are filled with the same amount of ice. The containers are made of different metals. If the ice in both containers melts in $20$ minutes and $35$ minutes respectively,find the ratio of their thermal conductivities.

$A$ brass boiler has a base area of $0.15\; m^{2}$ and thickness $1.0\; cm$. It boils water at the rate of $6.0\; kg/min$ when placed on a gas stove. Estimate the temperature (in $^oC$) of the part of the flame in contact with the boiler. Thermal conductivity of brass $= 109\; J s^{-1} m^{-1} K^{-1}$; Heat of vaporisation of water $= 2256 \times 10^{3}\; J kg^{-1}$.

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

If the thermal conductivity of aluminum is $0.5 \ cal/cm \cdot s \cdot ^\circ C$,then the temperature gradient required to conduct $10 \ cal/s \cdot cm^2$ in the steady state is ...... $^\circ C/cm$.

Four identical conducting rods are joined to form a square $ABCD$. The temperatures of junctions $A, B,$ and $C$ are maintained at $100^{\circ}C, 40^{\circ}C,$ and $0^{\circ}C$ respectively. Choose the $\text{INCORRECT}$ statement for this arrangement in a steady state. (The value of $\frac{KA}{L} = 1 \text{ J}/(s \cdot ^{\circ}C)$).

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is