【讨论】清华大学教授给出的思考题！高等热力学难题！ - 能源 - 工程热物理

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西湖酷鱼

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zongyu_1986(金币+1):感谢这位朋友的热心帮助，欢迎常来理工农林 2010-12-19 09:13:28

然后，刚敲完上面那段，就在wiki上面找到解释了，如下：

Maxwell equal area rule

Below the critical temperature (T’ < 1) an isotherm of the Van der Waals equation oscillates as shown.
Maxwell's rule eliminates the oscillating behavior of the isotherm in the phase transition zone by defining it as a certain isobar in that zone.

Along the red portion of the isotherm \scriptstyle \left({{\partial P'}/{\partial V'}}\right)_{T'}>0 which is unstable; the Van der Waals equation fails to describe real substances in this region. To fix this problem James Clerk Maxwell (1875) replaced the isotherm between a and c with a horizontal line positioned so that the areas of the two hatched regions are equal. The flat line portion of the isotherm now corresponds to liquid-vapor equilibrium. The portions a–d and c–e are interpreted as metastable states of super-heated liquid and super-cooled vapor respectively.[3]

Maxwell justified the rule by saying that work done on the system in going from c to b should equal work released on going from a to b. (Area on a PV diagram corresponds to mechanical work). That’s because the change in the free energy function A(T,V) equals the work done during a reversible process the free energy function being a state variable should take on a unique value regardless of path. In particular, the value of A at point b should calculate the same regardless of whether the path came from left or right, or went straight across the horizontal isotherm or around the original Van der Waals isotherm. Maxwell’s argument is not totally convincing since it requires a reversible path through a region of thermodynamic instability. Nevertheless, more subtle arguments based on modern theories of phase equilibrium seem to confirm the Maxwell Equal Area construction and it remains a valid modification of the Van der Waals equation of state.[4]

The Maxwell equal area rule can be derived from an assumption of equal chemical potential μ of coexisting liquid and vapour phases[5].

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Keepmoving!

21楼2010-10-18 14:13:24

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http://en.wikipedia.org/wiki/Van_der_Waals_equation

楼主同学你仔细看看那句“To fix this problem James Clerk Maxwell (1875) replaced the isotherm between a and c with a horizontal line positioned so that the areas of the two hatched regions are equal.”就是说，除了范式方程式人造的，这段“真实汽液”的等压线也是构造出来，目的就是为了让两个面积相等。

The Maxwell equal area rule can be derived from an assumption of equal chemical potential μ of coexisting liquid and vapour phases[5].

最后这句就更清楚了，就是用汽液相平衡来证明，但是我觉得这简直是循环论证了。。。因为这条水平线就是为了两个面积相等而构造的。

A E Elhassan, R J B Craven, K M de Reuck, The Area Method for pure fluids and an analysis of the two-phase region, Fluid Phase Equilibria 130 (1997) 167-187.

Anyway,找到1997年的这篇文章就是你要的答案了。

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22楼2010-10-18 14:17:11

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引用回帖:

Originally posted by 西湖酷鱼 at 2010-10-18 14:17:11:
http://en.wikipedia.org/wiki/Van_der_Waals_equation

楼主同学你仔细看看那句“To fix this problem James Clerk Maxwell (1875) replaced the isotherm between a and c with a horizontal line ...

是啊，那条等温线就是人为构造出来的，以使二者面积相等！但是，这里面有
道理的，那就是吉布斯函数在两相是相等的。

[ Last edited by 能源小蚂蚁 on 2010-10-19 at 23:58 ]

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23楼2010-10-18 23:23:58

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