对等温条件下理想气体伯努利方程的讨论

A DISCUSSION ON THE BERNOULLI’S EQUATION OF IDEAL GAS UNDER ISOTHERMAL CONDITION

在普通物理中一般只介绍理想流体的伯努利方程。由于气体具有显著的可压缩性,定量分析气体参量和流速的关系时还应考虑密度变化的影响。当气体与热库良好地接触,且膨胀和压缩过程进行得较为缓慢时可以视为等温过程。在《等温条件下可压缩理想气体的伯努利方程》一文中利用能量守恒导出了等温条件下理想气体满足的伯努利方程,但在推导过程中由于忽略了气体与外界的热传递导致结果存在问题。本文指出了其不当之处,用两种方法给出了正确的推导,并基于导出的结果简要讨论了气体压强与流速的关系。

Typically,only the Bernoulli’s equation of ideal fluid is introduced in general physics.To quantitatively analyze the relation between the parameters and flow speed of gas,it is also necessary to take the effect of density variation into account due to its significant compressibility.The process can be considered to be isothermal,when the gas is in good contact with a thermal reservoir,and its expansion and compression are slow.The Bernoulli’s equation of ideal gas under isothermal condition is derived by the law of conservation of energy in the paper titled"The Bernoulli’s equation of compressible ideal gas under the isothermal condition".However,the result is problematic due to the neglect of heat transfer between gas and surroundings.The error of the above paper is pointed out and the correct derivation is given in two methods,the relation of pressure and flow velocity is also briefly discussed based on the derived result.