The derivation of thermodynamical relations for a simple system

دسته بندی: ترمودینامیک و مکانیک آماری
ویرایش:  
نویسندگان: Shaw A.N.  
سری:  
 
ناشر:  
سال نشر:  
تعداد صفحات: 39 
زبان: English 
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) 
حجم فایل: 4 مگابایت 

قیمت کتاب (تومان) : 56,000

مقاله علمی / فیل. ترانس. روی. Soc. لندن. الف، 1935، جلد. 234، صفحات 299-328. در اکثر مقالات و متونی که نیاز به یا توضیح کاربردهای ترمودینامیک دارند، روابط متعددی بین مشتقات جزئی به دست آمده یا بدون اتخاذ یک روش سیستماتیک تاکنون هیچ رویه یکسانی برای یافتن سریع و آسان رابطه بین هر مشتق معین و هر مجموعه مجاز دیگر مشتقات انتخاب شده برای مرجع دنبال نشده است. رویه بسیار رایجی برای برخورد با روابط مفید با روش «ارائه و به دنبال آن تأیید» وجود دارد که رضایت‌بخش‌تر است. چند جدول موجود است. به طور خاص، "مجموعه متراکم فرمول های ترمودینامیکی"، توسط P.W. Bridgman (مطبوعات دانشگاه هاروارد) مفید است و طیف وسیعی را پوشش می دهد. اما در همه رویه‌های کنونی، وظیفه بیان یک مشتق جزئی اول یا دوم بر حسب مجموعه‌ای از موارد دیگر، به طور کلی بسیار پر زحمت است. در مواردی که مشتقات مختلف یک مجموعه مرجع انتخابی دارای جفت متغیرهای مستقل متفاوتی بودند، بسیاری از تبدیل‌های مورد علاقه احتمالی به‌عنوان کاملاً پیچیده یا برای حل بسیار خسته‌کننده نادیده گرفته شدند.

Scientific article / Phil. Trans. Roy. Soc. Lond. A, 1935, Vol. 234, pp. 299–328. In the majority of articles and texts requiring or explaining the applications of thermodynamics, numerous relations between partial derivatives are obtained or discussed without the adoption of a systematic method. No uniform procedure has been followed heretofore for finding quickly and easily the relation between any given derivative, and any permissible set of other derivatives chosen for reference. There is a very common practice of dealing with useful relations by the method of 'presentation followed by verification', which is most unsatisfactory. A few tables are available; in particular, the 'Condensed Collection of Thermodynamical Formulas', by P.W. Bridgman (Harvard Univ. Press) is useful and covers a large range; but in all current procedures the task of expressing a first or second partial derivative in terms of a set of others, remains in general most laborious. In the cases when the various derivatives of a chosen reference set had different pairs of independent variables, many transformations of possible interest have been neglected as altogether too complicated or too tedious for solution. If we desire to evaluate some partial derivative which cannot be obtained directly from experimental data, we should naturally choose other derivatives which have been found with the desired precision, and use them to calculate the former. Curiously, it appears that little advantage is taken of this possible procedure; often we find that the better-known standard relations are used, when the included derivatives may not have been determined with as high a precision as some others. With the aid of a simple Jacobian notation, it is the object of this paper to outline a systematic direct procedure capable of effecting any desired transformations and yielding many millions of relations with a minimum of analysis. This may be facilitated by two or three tables, which, while much more compact than previously existing ones, contain data for a great many more transformations. The derivation of these tables will be found straightforward, and the art of using them easily, may be acquired rapidly. Throughout this article our attention will be confined to the case of a simple system, under circumstances where three related thermodynamical variables are sufficient to describe its state. The extension to cases involving change of mass may be developed along similar fines later. It was considered essential to present this type of work in a sufficiently elementary manner and with adequate instructions, so that it might be of immediate use to teachers and students of thermodynamics as well as to those who will apply it in physics, chemistry, and engineering.