Thermodynamics in mineral sciences : an introduction by Ladislav Cemic

By Ladislav Cemic

This publication offers the elemental rules of thermodynamics for geosciences, in response to the author’s personal classes over a couple of years. Many examples support to appreciate how mineralogical difficulties will be solved through utilizing thermodynamic principles.

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0 0 1 2 3 4 5 P[GPa] Fig. 5 Volume of kyanite as a function of pressure at room temperature (Yang et al. 1997). Example 3: The volume of the unit-cell versus pressure curve for chlorite (see Fig. 3) shows a significant curvature. This means that the compressibility coefficient is pressure dependent within regime under consideration. In order to account for this behavior, a polynomial of the second-order is fitted to the data. 1601P ; P[GPa]. 1 Volume of pure phases 33 Using this polynomium, the compressibility coefficient can be calculated at any a pressure within the pressure range over which the volume-pressure relationship was measured.

In the case of a triclinic substance Eq. 57) z ¯ ¿ where D, E, and J are the angles between the vectors b and c , a and c , a and b , respectively. Example: Yang et al. 000°. The unit cell of kyanite contains 4 formula units. 157 cm mol . For a monoclinic system, where only one angle (E) differs from 90°, Eq. 58) Example: Diopside, CaMgSi2O6, possesses a monoclinic structure, C2/c. 899° (Tribaudino et al. 2000). Each unit cell contains 4 formula units of diopside. Its molar volume is calculated according to Eq.

15 K. 902 cm mol –1 for the molar volume at 700 K. 4 400 600 800 1000 T[K] Fig. 4 GPa (Zhang et al. 2002). A straight line and a second-order polynomial are fitted to the data points. 30 2 Volume as a state function In this example 700 K is taken as the upper temperature limit. Because of the assumed linear behavior, the choice of upper temperature is entirely arbitrary. Hence, any other temperature within the measured interval could have been used as well. 43 u10 K . If one uses a second-order polynomial of the form V = a + bT + cT2, instead of a straight line, a much better fit is obtained.

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