### Statistical Mechanics Lecture 5 of 29

April 10, 2012 by Antonello Scardicchio

A. Scardicchio, ICTP

In this lesson the first incursion into phase transitions was taken. Isotherms in the ideal gas P - V diagram for the liquid - gas transition were discussed. The critical isotherm, which includes the critical point, divides two regions in the P - V plane. Below it, the ideal gas The Clapeyron equation was derived from the First and Second Laws.

The van der Waals equation of state was introduced. This is an equation of state for a gas which, as opposed to the ideal gas, presents a phase transition. The van der Waals equation corrects the ideal gas e.o.s in two aspects. First, it takes into account the finite size of the gas molecules. Second it reflects the repulsive/attractive forces between molecules at short/large distances. Finally, the entropy of a van der Waals gas was calculated and the adiabatic process was written in several, equivalent forms.

In lesson 4, it was explained that there exists a critical isotherm, above which the liquid and vapor phases of an ideal gas are indistinguishable. What about a liquid - solid phase transition? Does such an isotherm exists? Try to provide a justification for your answer.

Maybe you've heard that the reason why ice skating is possible is that the applied pressure lowers the melting temperature of water. Thus, a thin film of liquid water is created through which the ice skates glide.

Check whether there is truth in this conventional wisdom estimating by how much the melting temperature of the water under the skates of a human skater is lowered. Do a Fermi calculation. You will - probably - need the latent heat of water.

Estimate the minimal mass of a glacier that flows mainly through basal sliding.

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