en>Cmglee: /* Explanation */ Use LaTeX math

2013-01-03T19:26:09Z

Explanation: Use LaTeX math

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{{orphan|date=December 2009}}

The '''Simon–Glatzel equation'''<ref>Simon F. E., Glatzel G., Z. Anorg. (Allg.) Chem., '''1929''', 178, 309-312</ref> 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 ==
<math>T_M = T_{Ref} \left( \frac{ P_M - P_{Ref} }{a} + 1 \right)^\frac{1}{c}</math>

TRef and PRef 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 PRef is then set to 0. ''a'' and ''c'' are adjustable and component specific parameters.

== Example parameters ==
[[File:Simon-Glatzel equation.png|Methanol melting temperatures|thumb]]
For [[Methanol]] the following parameters<ref>[[Dortmund Data Bank]]</ref> can be obtained:

{| class="wikitable" border="1"
|-
| 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 TRef = TM = 174.61 K and the reference pressure PRef 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.<ref>Kechin V.V., J. Phys. Condens. Matter, '''1995''', 7, 531-535</ref>

== References ==
{{reflist}}

{{DEFAULTSORT:Simon-Glatzel equation}}
[[Category:Phase transitions]]
[[Category:Equations]]

Relative purchasing power parity - Revision history

en>Cmglee: /* Explanation */ Use LaTeX math