Relative purchasing power parity

The Simon–Glatzel equation is an empirical correlation describing the pressure dependence of the melting temperature. The pressure dependence of the melting temperature is small for small pressure changes because the volume change during fusion or melting is rather small. But very high pressures have a significant effect because the liquid has (normally) a larger volume than the solid and a higher pressure makes the melting thermodynamically unfavorable and leads therefore to a higher melting temperature. If the liquid has a smaller volume than the solid (as for ice and liquid water) a higher pressure leads to a lower melting point.

The equation

$T_M=T_{Ref}{(\frac{P_M-P_{Ref}}{a}+1)}^{\frac{1}{c}}$

T_Ref and P_Ref are normally the temperature and the pressure of the triple point, but the normal melting temperature at atmospheric pressure are also commonly used as reference point because the normal melting point is much easier accessible. Typically P_Ref is then set to 0. a and c are adjustable and component specific parameters.

Example parameters

Methanol melting temperatures

For Methanol the following parameters can be obtained:

a	188158	kPa
a	188.158	MPa
c	5.15905
Tmin	174.61	K
Tmax	228.45	K
Pmax	575000	kPa
Pmax	575.000	MPa

The reference temperature has been T_Ref = T_M = 174.61 K and the reference pressure P_Ref has been set to 0 kPa.

Methanol is a component where the Simon-Glatzel works well in the given validity range. The Simon–Glatzel equation cannot be used if the melting curve is falling or has maximums.

References

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