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. At 1 atm pressure, ice melts at 273.15 K, 6010. Jmol^-1, ΔH _fusion = the density of ice is 920. kgm⁻³, and the density of liquid water is 997 kgm⁻³.

a. What pressure is required to lower the melting temperature by 4.0°C?

b. Assume that the width of the skate in contact with the ice has been reduced by sharpening to 19 × 10⁻³ cm, and that the length of the contact area is 18 cm. If a skater of mass 78 kg is balanced on one skate, what pressure is exerted at the interface of the skate and the ice?

c. What is the melting point of ice under this pressure?

d. If the temperature of the ice is −4.0°C, do you expect melting of the ice at the ice–skate interface to occur?