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On the concept of thermodynamic space
ZHANG Qi'nan
School of Aeronautical Science and Engineering, Beihang University, Beijing 100083, China
Received: 2016-10-18; Revised: 2017-04-16; Accepted: 2017-05-05; Published online: 2017-05-12 15:49
Corresponding author. ZHANG Qi'na, E-mail:qal@buaa.edu.cn
Abstract: In the study of pneumatics, it is inevitable to refer to the basic laws of thermodynamics. In the past, a number of engineering authors often wrote heat Q and the micro-increments of the work done by the gas W as dQ and dW, which are, however, not correct expressions as far as a strict mathematical theory is concerned. When participating in the editing of the Aviation Air Force Manual, the author raised this issue. In the second edition of the manual, dQ and dW were corrected to δW and δQ. But some pneumatic works still fail to pay attention to the problem, and are still used to using dQ and dW. In this article, a rigorous proof is conducted and the concept of the thermodynamic space is proposed to clarify the confusion in the past.
Key words: thermodynamic space     geometric space     status parameter     integral-total differential condition     differential-total differential condition
1 全微分存在的条件

P、Q、Rx、y、z 3个自变量在单连通域中的连续函数，而且都存在连续的偏导数。和式Pdx+Qdy+Rdz是某函数F(xyz)的全微分的必要充分条件为

1) 积分型条件

 （1）

2) 微分型条件

 （2）

2 热力学第一定律

 （3）

 （4）

 （5）

 （6）

 （7）

3 焓和熵的概念

 （8）

 （9）

 （10）

 （11）

 （12）

4 热力学第二定律

5 结论

 （13）

 （14）

6 后记

http://dx.doi.org/10.7527/S1000-6893.2016.721356

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#### 文章信息

ZHANG Qi'nan

On the concept of thermodynamic space

Acta Aeronautica et Astronautica Sinica, 2017, 38(8): 721356.
http://dx.doi.org/10.7527/S1000-6893.2016.721356