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# 数学代写|信息论代写Information Theory代考|INF563 Liquid–Gas Transition

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## 数学代写|信息论代写Information Theory代考|Liquid–Gas Transition

The line LG in Fig. 2.9 is the line along which liquid and gaseous phases coexist. In this case the slope of the curve is also positive. Both the entropy and the volume change in the vaporization processes are positive. Again, traditionally the entropy of vaporization is interpreted in terms of order-disorder. This interpretation is unfortunately incorrect. It is difficult to argue that gas is more disordered than liquid. The correct interpretation is again the change in the accessible volume per particle, and the weakening of the average intermolecular interactions in the process of the evaporation, hence $\Delta S_v>0$.

It is worthwhile to mention an empirical law known as the Trouton Law. It states that the entropy of vaporization at one atmospheric pressure of many liquids is almost constant;
$$\Delta S_v \approx 85-87 / \mathrm{Jmol}^{-1} K^{-1}$$
Table 2.1 shows a few values of the entropy of vaporization. Note that the values of $\Delta S_v$ for liquids with strong interactions, such as water, ethanol, and methanol, are much larger than the values for the other liquids.

## 数学代写|信息论代写Information Theory代考|Solid–Liquid Transition

The solid-liquid coexistence curve is denoted by SL in Fig. 2.9. In the transition from the solid to the liquid, the entropy-change is always positive. Again, this is traditionally interpreted in terms of transition from order to disorder phases. Although it is certainly true that a solid is more ordered than a liquid, this fact has nothing to do with the positive change in entropy. The change in entropy is due to the change in the total interaction energy among the particles. Unlike the transition from solid to gas where there is a huge change in volume, in the solid to liquid phase the change in volume is usually quite small. This is the reason for the large slope of the curve $\mathrm{LG}$ in Fig. 2.9a.
The slope is given by the quotation:
$$\left(\frac{d P}{d T}\right)_{e q}=\frac{\Delta S_m}{\Delta V_m}$$
where $\Delta S_m$ and $\Delta V_m$ are the change in the molar entropy and the volume in the process of melting $(m)$. It should be noted that $\Delta S_m$ is always positive, and $\Delta V_m$ is positive for most substances. An anomalous case is water for which $\Delta V_m<0$, i.e. the molar volume of the liquid is smaller than that of ice. In this case the slope of the SL curve is negative, see Fig. 2.9b.

## 数学代写|信息论代写Information Theory代考|Liquid-Gas Transition

$$\Delta S_v \approx 85-87 / \mathrm{Jmol}^{-1} K^{-1}$$

## 数学代写|信息论代写Information Theory代考|Solid-Liquid Transition

$$\left(\frac{d P}{d T}\right)_{e q}=\frac{\Delta S_m}{\Delta V_m}$$

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