Question

3) A polystyrene container is filled to the brim with water at 0 0C and sealed with a polystyrene lid of the same thickness as the container. The sealed container is immersed in a reservoir of liquid Nitrogen at a temperature of 73 K. The surface area of the container is 5 x 10-2 m2 and the rate of heat flow from the inside to the outside of the container is 66 Watts. (a) Assuming the temperature of inner and outer surfaces of the container remain constant, what is the thickness of the polystyrene ? (6) [ Thermal conductivity of polystyrene = 0.033 Watts/m.K ; 0 0C = 273 K ] (b) If the mass of the water in the container is 0.75 kg, how long will it take for all the water inside to freeze ? [ Latent heat of fusion of water = 330 kJ/kg ] (5) (c) Calculate the entropy change of the water in the container as it freezes. Note that, despite my best efforts, the numbers in this case will not be “nice”, so don’t worry about evaluating a final numeric answer. Explain how/why the value you have determined is consistent with the 2nd Law of Thermodynamics. (5) An identical container is now filled to the brim with water is taken from a refrigerator at 5 0C. (d) If the volume of the water in the container is 7.5 x 10-4 m3 , assuming the ambient room temperature is 250C, how much water will overflow from the container ? (6) [ The coefficient of volume expansion of water between 5 0C and 25 0C is 2 x 10-4 K-1 ; Coefficient of volume expansion of polystyrene in the same temperature range = 8 x 10-5 K-1 ] (e) Suppose that instead of 5 0C the refrigerator cools the water to 1 0C and the ambient room temperature is 3 0C. How much, if any, water do you expect to overflow in this case ?

Answer 1