arXiv 1802.014742018-02cond-mat.stat-mech

绝热过程的范德瓦尔气体方程及其卡诺热机效率

Van der Waal's gas equation for an adiabatic process and its Carnot engine efficiency

Kiran S. Kumar, Aravind P. Babu, M. Ponmurugan

备注：: IAPT - Physics Education (Jul-Sep 2017)

摘要：

对于服从范德瓦尔状态方程的气体，已有许多研究。然而，在大学教科书和文献中，还没有对经历绝热过程的范德瓦尔气体进行具体和直接的研究。在绝热过程中，系统与其周围环境之间没有热能交换。本文发现绝热过程的范德瓦尔方程为$\left(P+\frac{n^2a}{V^2}\right) \left(V-nb\right)^Γ=\mbox{constant}$，其中$P$为压力，$V$为体积，$n$为范德瓦尔气体的摩尔数，$a$和$b$为范德瓦尔常数，$Γ$为联系定压定容比热的因子。我们明确地利用这个关系，得到了工质服从范德瓦尔状态方程的卡诺热机的效率。我们最简单的方法可以使大学生清楚地认识到$Γ$不同于理想气体的绝热过程的$γ$。我们还证明了卡诺热机的效率与工质无关。

英文摘要：

There has been many studies on gases which obeys Van der Waal's equation of state. However there is no specific and direct studies of Van der Waal's gas which undergoes adiabatic processes are available in the undergraduate text books and also in literature. In an adiabatic process there is no heat energy exchange between the system and its surroundings. In this article, we find that the Van der Waal's equation for the adiabatic process as $\left(P+\frac{n^2a}{V^2}\right) \left(V-nb\right)^Γ=\mbox{constant}$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles of the Van der Waal's gas, $a$ and $b$ are Van der Waal's constant and $Γ$ is a factor which relates the specific heat at constant pressure and at constant volume. We use this relation explicitly and obtained the efficiency of a Carnot engine whose working substance obeys Van der Waal's equation of state. Our simplest approach may provide clear idea to the undergraduate students that $Γ$ is different from $γ$ of the ideal gas for an adiabatic process. We also shown that the efficiency of the Carnot engine is independent of the working substance.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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