One of water's most familiar and unusual properties is its negative volume of
melting: the density of ice is 917 kg/m³ and that of liquid water is 1,000 kg/m³ at
the normal melting point. Some other useful properties of water for this problem
are $c_{p,ice} \approx 38 \text{ J/K mol}$, $c_{p,liq.} \approx 75 \text{ J/K mol}$, $\Delta h_m \approx 6 \text{ kJ/mol}$ at $0^\circ C$, and
$M_{H_2O} \approx 18 \text{ g/mol}$.
(a) It has been claimed that ice skating is possible because the pressure of the
blade on the ice lowers its freezing point, induces melting, and provides a
slippery liquid layer. What is the expected freezing temperature for a 65-kg
person on skates that have a total area in contact with the ice of 30 cm²
(blades 0.5 cm wide and 30 cm long)? Is it likely the ice will actually melt?