Simultaneous Temperature and Pressure Dependence

There is nothing stopping us from expanding our ideas to transformations in which temperature and pressure change simultaneously. In this case the chemical potential can be expressed as follows  

The dependence of transition temperatures upon pressure can be described by these equations as well. Here is a familiar example representative of many others. Ice 

As mentioned, water is among the few exceptions where in the solid state is greater than in the liquid state. This special characteristic of ice is responsible for the ability of a glacier to flow downward a few meters per day in a moimtain valley like slow moving dough. Where the ice is under especially high pressure, it melts and becomes pliable so that it gradually moves around obstacles. 

To illustrate this, let us take a look at Fig. 5.9. If the pressure is increased, the chemical potentials of the solid and the hquid phase increase, but this increase is much more pronounced for the solid than for the liquid phase [because of 0 / (B l) /5(B s)]. Thus the intersection point of the curves (Tsi) shifts to the left, i.e., the freezing point is lowered by 

It is easy to calculate the lowering of temperature in compressed ice, i.e., the freezing-point depression of water under pressure. The condition for equilibrium /is = Pi takes the following form  

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Finally, a simultaneous temperature and pressure dependence can be described by the following combined equation. 

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