Question

An ice skate is able to glide over the ice because the skate blade exerts sufficient pressure on the ice that a thin layer of ice is melted. The skate blade then glides over this thin melted water layer. Determine the pressure an ice skate blade must exert to allow smooth ice skate at – 10°C. 

The following data is given for the range of temperatures and pressures involved : 

h_fg(ice) = 334 kJ/kg ; v_liq. = 1 × 10 m³/kg ; v_ice = 1.01 × 10³ m³/kg.

Answer 1

Since it is a problem of phase change from solid to liquid, therefore, we can use Clausius- Claperyon equation given below :

\(\cfrac{dp}{dT}\) = \(\cfrac{h_{fg}}{v_{fg}}\) . \(\cfrac 1T\)

Multiplying both the sides by dT and integrating, we get

Substituting these values in eqn. (i), we get

This pressure is considerably high. It can be achieved with ice skate blade by having only a small portion of the blade surface in contact with the ice at any given time. If the temperature drops lower than – 10°C, say – 15°C, then it is not possible to generate sufficient pressure to melt the ice and conventional ice skating will not be possible.