Two vessels made of different materials are identical in size and wall-thickness. They are filled with equal quantities of ice at $0^{\circ }C$. Compare the coefficients of thermal conductivity of the materials of the vessels. When the ice melts completely in 10 and 25 minutes respectively.

A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of 0.1 gm of ice per second. If the rod is replaced by another rod with half the length and double the radius of the first and if the thermal conductivity of the material of the second rod is 0.25 times that of first, the rate at which ice melts in gm/second will be :

In the steady state of temperature at the end of a copper rod of length $25cm$ and area of cross-section $1.0c{m}^2 are {125}^{\circ }C and 0^{\circ }C$ respectively. Calculate the temperature gradient, rate of heat flow and the temperature at a distance $10cm$ from the hot end. $[K for copper =9.2\times {10}^{-3} kilocal/m{ }^{\circ }C-s]$

Latent heat of vaporization of water$=2\cdot 26\times {10}^6 Jk{g}^{-1}.$ when water is boiled in a container having a bottom of surface area $25c{m}^2$, thickness $1\cdot 0mm$ and thermal conductivity $50 W{m}^{-10}{C}^{-1}.$ $100g$ of water is converted into steam per minute in the steady state after the boiling starts. Assuming that no heat is lost to the atmosphere, calculate the temperature of the lower surface of the bottom. $$

The area of glass of a window of a room is $10 m^2$ and thickness is $2mm.$The outer and inner temperatures are $40°C$and $20°C$ respectively. Thermal conductivity of glass in S.I unit is$0.2.$ The heat flowing in the room per second will be :

A thermally isolated vessel contains $100g$of water at $0°C$ When air above the wall pumped out, some of the water freezes and some evaporates at $0°C$ itself. Calculate the number of the ice formed if no water is left in the vessel. Latent heat of vaporization of water $0°C=\times {10}^{6}Jkg-1$ and latent heat of fusion of ice $=3.36\times {10}^{5}Jkg-1$

A slab of stone of area $3600{ \mathrm{cm}}^2$ and thickness $10 \mathrm{cm}$ is exposed on the lower surface to steam at $100°\mathrm{C}$. A block of ice at $0°\mathrm{C}$ rests on the upper surface of the slab. In one hour, $4.8 \mathrm{kg}$ of ice is melted. The thermal conductivity of the stone in $J{S}^{-1}{m}^{-1}{K}^{-1}$. Latent heat of ice $=3.36\times {10}^5{\mathrm{Jkg}}^{-1}$.