Problem on melting of ice

Question

A) It has been suggested that the surface melting of ice plays a role in enabling speed skaters to achieve peak performance. Carry out the following calculation to test this hypothesis. Suppose that the width of the skate in contact with the ice has been reduced by sharpening to 0.25 mm. and that the length of the contact area is 15 cm.

i) If a skater of mass 85 kg is balanced on one skate, what pressure (in bar) is exerted at the interface of the skate and ice?

ii) If the temperature of the ice is -5.0°C, do you expect melting of the ice at the ice-skate interface to occur? Why?

B) At what temperature does water boil on the top of Mount Everest, the elevation h = 8848m? Use only the following information to obtain your estimate:

-Dependence of pressure with the altitude is given by

P = P_atm exp [(-MW_gh)/RT]

where, P_atm is atmospheric pressure, g is the gravitational acceleration, MW is the molecular weight of air and T is average temperature (=273 K).

-Normal boiling point (B.P.) of water is 100°C.

-The latent heat of vaporization of the water is 2257 KJ/Kg.