# Rüchardt實驗

Rüchardt實驗是测定理想气体绝热指数（即理想气体恒压热容恒容热容之比）的一个著名实验。[1][2][3]该实验最早由Eduard Rüchardt (March 29, 1888 – March 7, 1962)引入，通过测定绝热气缸上活塞的微振动周期，从而得出绝热指数的数值。

## 原理

Rüchardt實驗装置示意图

${\displaystyle F=A\mathrm {d} P}$

${\displaystyle a={\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}={\frac {A}{m}}\mathrm {d} P}$

${\displaystyle V^{\gamma }\mathrm {d} P+\gamma PV^{\gamma -1}\mathrm {d} V=0}$

${\displaystyle \mathrm {d} P=-{\frac {\gamma P}{V}}\mathrm {d} V}$

${\displaystyle \mathrm {d} V=Ax}$

${\displaystyle {\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+{\frac {\gamma PA^{2}}{mV}}x=0}$

${\displaystyle T={\frac {2\pi }{\omega }}=2\pi {\sqrt {\frac {mV}{\gamma P{A}^{2}}}}}$

${\displaystyle {\gamma }={\frac {4\pi ^{2}mV}{A^{2}PT^{2}}}}$

## 参考文献

1. ^ Fuchs, Hans U. The Dynamics of Heat: A Unified Approach to Thermodynamics and Heat Transfer, 2010, P212-214
2. ^ Glasser, L. Useful papers on Ruchardt's method. Journal of Chemical Education. 1990, 67 (8): 720. Bibcode:1990JChEd..67..720G. doi:10.1021/ed067p720.3.
3. ^ Rüchardt, E. Physikalische Zeitschrift. 1929, 30: 58–59. 缺少或|title=为空 (帮助)
4. ^ Kinetic theory of gases (PDF). ld-didactic.de. [5 Nov 2013]. （原始内容存档 (PDF)于2013-11-05）.