A thin metallic shell of negligible thickness and radius 'a' has water at `0^0`C is completely filled inside it. This metallic shell is kept in an environment of -`theta ^0` C .The time after which `frac{1}{8} ^(th)` of the volume of water is left and rest of the water freezes will be (Given conductivity of ice K Latin heat of fusion L density of ice `rho`.

A layer of ice of thickness y is on the surface of a lake. The air is at a constant temperature -theta^@C and the ice water interface is at 0^@C . Show that the rate at which the thickness increases is given by (dy)/(dt) = (Ktheta)/(Lrhoy) where, K is the thermal conductivity of the ice, L the latent heat of fusion and rho is the density of the ice.

On a cold winter day, the atmospheric temperature is -theta (on celsius scale) which is below 0^(@)C . A cylindrical drum of height h made of a bad conductor is completely filled with water at 0^(@)C and is kept outside without any lid. Calculate the time taken for the whole mass of water to freeze. Thermal conductivity of ice is K and its latent heat of fusion is L . Neglect expansion of water on freezing.

A copper rod of length 60 cm long and 8 mm in radius is taken and its one end is kept in boiling water and the other end in ice at 0^(@) C . If 72 gm of ice melts in one hour with is the thermal conductivity of copper ? Latent of fusion of ice = 336 "KJ/Kg" .

When 1 g of ice at 0^(@)C melts to form 1 g of water at 0^(@)C then, is the latent heat absorbed by the ice or given out by it?

A metallic cylindrical vessel whose inner and outer radii are r_1 and r_2 is filled with ice at 0^@C . The mass of the ice in the cylinder is m. Circular portions of the cylinder is sealed with completely adiabatic walls. The vessel is kept in air. Temperature of the air is 50^@C . How long will it take for the ice to melt completely. Thermal conductivity of the cylinder is K and its length is l. Latent heat of fusion of L.

An ice cube floats in water. What percentage of volume is outside water. Density of water = 1g// c c , density of ice = 0.9 g// c c .

An icebox almost completely filled with ice at 0^(@)C is dipped into a large volume of water at 20^(@)C . The box has walls of surface area 2400cm^(2) thickness 2.0mm and thermal conductivity 0.06Wm^(-1)C^(-1) . Calculate the rate at which the ice melts in the box. Latent heat of fusion of ice =3.4xx10^(5)Jkg^(-1) .

A thermally isolated vessel contains 100g of water at 0^(@)C . When air above the water is pumped out, some of the water freezes and some evaporates at 0^(@)C itself. Calculate the mass of the ice formed such that no water is left in the vessel. Latent heat of vaporization of water at 0^(@)C=2.10xx10^(6)J//kg and latent heat of fusion of ice =3.36xx10^(5)J//kg .

What will be the final temperature when 150 g of ice at 0^@C is mixed with 300 g of water at 50^@C . Specific heat of water =1 cal//g//^@C . Latent heat of fusion of ice =80 cal//g .

One side of an iron plate one metre square is kept at 100°C and the other side is at 0°C. The thickness of the plate is 1 cm. If all the heat conducted across the plate in one minute is used in melting ice, calculate the amount of ice so melted. Thermal conductivity of iron = 0.162 in C.G.S. unit L.H. of fusion of ice = 80 cal/gm.