Problem 32P

The density of ice is 917 kg/m3.

(a) Use the Clausius-Clapeyron relation to explain why the slope of the phase boundary between water and ice is negative.

(b) How much pressure would you have to put on an ice cube to make it melt at –1°C?

(c) Approximately how deep under a glacier would you have to be before the weight of the ice above gives the pressure you found in part (b)? (Note that the pressure can be greater at some locations, as where the glacier flows over a protruding rock.)

(d) Make a rough estimate of the pressure under the blade of an ice skate, and calculate the melting temperature of ice at this pressure. Some authors have claimed that skaters glide with very little friction because the increased pressure under the blade melts the ice to create a thin layer of water. What do you think of this explanation?

Density and Pressure Fluids Liquids incompressible Gases compressible Particle Density: Pparticle/V Density: p= M/V Pressure: P= F/A Hydrostatic (liquid at rest) (no order kinetic energy) Pbottom Ptop= pgΔh Pbottom P top+ pg(h toph bottom F – F = mg top bottom Units: 1 atm= 101 kPa= 14.7 pounds per square inch M= pv M=pAh Pascal’s law: Any change in the pressure at the surface is transmitted to every point in the liquid P is the same everywhere at the same time Buoyancy An object partially or wholly immersed in a gas or liquid is acted upon by an upward buoyant force B equal in magnitude to the weight w of the gas or liquid it displaces o For the magnitude