EOS
Tittle
Despite its popularity, the well-known equation attributed to Tait has several undesirable features; moreover, it is in fact not Tait’s original equation, but is the result of an accidental misquotation by a later writer. …
The subject of compressibility equations for liquids is really a very simple one, Unfortunately, it has been so badly treated in the literature that it has been made to appear unnecessarily complex, and the resulting confusion has had at least one serious consequence. …
To meet this need it is necessary to employ some empirical equation, the sole justification for which is that it works. …
Since all three equations are equally accurate within the pressure range that concerns the great majority of workers, the choice between them can be governed by convenience. …The use of this equation (equation (5)) is also in harmony with the philosophical principle of Occam’s razor, …
It is therefore most surprising to find that there has been an almost universal preference for the so-called Tait equation (6). This and (4) are both very inconvenient to use in practice because both K and K‘ involve a differential coefficient which cannot easily be evaluated from experimental readings.
The primary reason for the choice of this equation (equation (5)) has already been given: its great simplicity of application. A second valuable feature of this equation is that its two constants have an easily grasped physical significance. …
Present-day users of the equation to which his name is nowadays attached may find it hard to believe that this is not the equation that Tait proposed, …
It will never be known for certain who it was that first misquoted Tait. …
The fact is that hundreds of authorities during the past sixty years have blindly followed Tammann and used this inferior equation instead of the true Tait equation, so that Tammann probably deserves to be regarded as the perpetrator of one of the most far-reaching misquotations in the history of physics. …
It cannot be emphasized too strongly that this equation has no advantages over the linear secant-modulus equation, and has a number of serious disadvantages. It is much less convenient to use, its constants have no obvious physical meaning, it does not give rise to simple expressions, …
This last statement is, of course, in conflict with the views of various modern writers who have extolled the virtues of the spurious Tait equation. Some of them have quoted the following table from Tait’s papers as an alleged proof of the accuracy of the spurious Tait equation. …
Reference to Tait’s original paper (Tait 1900, pp. 334-8) reveals, of course, that he based his calculations upon his own equation (equation (14)), so that this table is really a confirmation of the linear secant-modulus equation, and not of the spurious Tait equation. …
Although there is no reason why the spurious Tait equation should continue in use in the future, a great deal of work in the past has been published in terms of the two constants in this equation. It is therefore fortunate that these two constants can easily be converted to the two constants in the linear secant-modulus equation.
Consequently, the observation which has frequently been made about C in the spurious Tait equation-that it is approximately the same for nearly all organic liquids at any temperature-applies also to the constant in in the linear secant-modulus equation. …
There is almost endless scope for constructing complicated compressibility equations, which work merely because they virtually coincide with the linear secant-modulus equation at relatively low pressures. …
(b) The well-known equation to which Tait’s name has been attached is not a desirable equation, and was certainly not propounded by Tait. It appears to have originated through an unfortunate misquotation by Tammann of Tait’s original equation (which was actually the linear secant-modulus equation expressed in reciprocal form). Relationships have been derived between the so-called Tait constants and the constants in the linear secant-modulus equation, thus enabling results expressed in one form to be re-expressed in the other.
尽管广为人知，这道归功于泰特的著名方程却存在若干缺陷；更何况它实际上并非泰特的原始公式，而是后世学者误引所致的偶然结果。…
液体压缩性方程的主题其实非常简单，遗憾的是，文献中对此的处理如此糟糕，以至于使其显得不必要地复杂，由此造成的混乱至少导致了一个严重后果。…
为满足这一需求，必须采用某些经验方程，其唯一依据在于其有效性。…
由于这三组方程在绝大多数工人所关注的压力范围内具有同等精度，因此选择哪组方程可根据实际操作的便利性来决定。…该方程（方程5）应用也符合奥卡姆剃刀的哲学原则。…
因此，令人惊讶的是，人们几乎普遍偏爱所谓的泰特方程（6）。这与(4)在实际应用中都极为不便，因为K和K’都涉及微分系数，而该系数难以通过实验读数直接测得。
选择该方程（方程5）的主要原因已阐明：其应用极为简便。该方程的另一重要优点在于其两个常数具有易于理解的物理意义。…
现在使用他名字命名的方程式的人很难相信这不是泰特提出的方程式，…
我们永远无法确定谁第一个错误引用了泰特。 …
事实上，在过去的60年里，数百名权威人士盲目地追随 Tammann ，并使用这个劣等方程式，而不是真正的泰特方程式，因此Tammann可能应该被视为物理学史上最深远的错误引用之一的肇事者。…
必须强调的是，该方程相较于线性正切模量方程并无优势，且存在诸多严重缺陷。。它使用起来不太方便，它的常数没有明显的物理意义，也无法推导出简洁的表达式，……
当然，这最后一种说法与许多现代学者的观点相冲突，这些学者歌颂虚假的泰特方程式的优点。其中一些人引用了Tait论文中的下表，作为虚假Tait方程准确性的证据。…
查阅泰特原始论文（Tait 1900, pp. 334-8）可知，他显然是基于自身推导的方程（方程(14)）进行计算的。因此该表格实质上是对线性切线模量方程的验证，而非对虚假的泰特方程的验证。
尽管没有理由继续使用伪Tait方程，但关于该方程中的两个常数，过去已经发表了大量的工作。因此，幸运的是，这两个常数可以很容易地转换为线性割线模量方程中的两个常数。
因此，关于伪泰特方程中C值的常见观察——即该值在任何温度下对几乎所有有机液体都近似相同——同样适用于线性割线模量方程中的常数。
构建复杂的压缩性方程几乎具有无限可能，这些方程之所以有效，仅仅是因为它们在相对较低的压力下几乎与线性切模量方程完全吻合。
（b） 泰特的名字所附的众所周知的方程不是一个理想的方程，当然也不是泰特提出的。它似乎源于Tammann对Tait原始方程（实际上是以倒数形式表示的线性割线模量方程）的不幸错误引用。已推导出所谓的Tait常数与线性割线模量方程中的常数之间的关系，从而使以一种形式表示的结果可以用另一种形式重新表示。
1 | @article{hayward1967, |