Question

You may have heard that ice skaters actually skate on a thin layer of water rather than solid ice (which reduces friction on the blade and allows them to skate faster). Let’s work through a calculation to determine if this statement is reasonable. Estimate the pressure exerted by a 200-lb hockey player, standing on two blades that are 0.1 mm x 20 cm. Calculate the melting point of ice below the player, assuming that the density of ice under these conditions is approximately 0.915 g cm^–3 and that of liquid water is 0.998 g cm^–3. Assuming a typical temperature of ice in a skating rink is 27 °F, does a hockey player skate on ice or water?

Answer 1

Pressure exerted by the player=force/area=mass*gravity/area

Here mass of the player=200lb=200 lb*0.453 kg/lb=90.718 kg

g=9.8 m/s^2

area of skate=0.1 *0.1cm*20cm=0.2 cm^2

Pressure=(90.718 kg)*(9.8 *100 cm/s^2)/0.2 cm^2=4445.182 *100 kg cm^-1s^2

Also pressure=Force*distance/area*distance=work done/volume =4445.182 *100 KJ/cm3

Now ,this pressure if is greater than the energy required per unit volume of ice for its conversion to water than surely ice must hv converted to water on application of this pressure.

temperature of ice=27 deg F=-2.8 deg C

energy required for conversion of 1cm3 of ice into water=energy for increase of ice temperature to 0 deg C+ enthalpy of fusion of ice=mass*heat capacity of ice*change of temperature+enthalpy of fusion of ice/water=0.915g/cm3 * 2.03J /g oC *(0-(-2.8deg C))+333.55 J/g =338.751 J

As the pressure applied is more than sufficient to convert ice into water ,the skater must be skating on a thin layer of water