A thin metallic shell of negligible thickness and radius 'a' has water at `0^0`C 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 `rho`.

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 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.

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" .

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.

A container of negligible heat capacity contains 1kg of water. It is connected by a steel rod of length 10m and area of cross-section 10cm^(2) to a large steam chamber which is maintained at 100^(@)C . If initial temperature of water is 0^(@)C , find the time after which it beomes 50^(@)C . (Neglect heat capacity of steel rod and assume no loss of heat to surroundings) (use table 3.1 , take specific heat of water =4180 J//kg.^(@)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 .

On a winter day when the atmospheric temperature drops to -10^(@)C , ice forms on the surface of a lake. (a) Calculate the rate of increases of thickness of the ice when 10cm of ice is already formed. (b) Calculate the total time taken in forming 10cm of ice. Assume that the temperature of the entire water reaches 0^(@)C before the ice starts forming. Density of water =1000kgm^(-3) , latent heat of fusion of ice =3.36xx10^(5)Jkg^(-1) and thermal conductivity of ice =1.7Wm^(-1)C^(-1) . Neglect the expansion of water on freezing.

A hollow sphere of glas whose external and internal radii are 11 cm and 9 cm respectively is completely filled with ice at 0^@C and placed in a bath of boiling water. How long will it take for the ice to melt completely? Given that density of ice = 0.9 g//cm^3 , latent heat of fusion of ice = 80 cal//g and thermal conductivity of glass =0.002 cal//cm-s^@C .

A 0.60 kg sample of water and a sample of ice are placed in two compartmetnts A and B separated by a conducting wall, in a thermally insulated container. The rate of heat transfer from the water to the ice through the conducting wall is constant P, until thermal equilibrium is reached. The temperature T of the liquid water and the ice are given in graph as functions of time t. Temperature of the compartments remain homogeneous during whole heat transfer process. Given specific heat of ice =2100 J//kg-K , specific heat of water =4200 J//kg-K , and latent heat of fusion of ice =3.3xx10^5 J//kg . Initial mass of the ice in the container equal to