重新定义理想气体系统的相空间解吉布斯方程
Redefining the Phase Space for Ideal Gas Systems Resolves the Gibbs Paradox
摘要：
对于一个在体积V内有N个分子的理想气体，每个分子在瞬时可到达的体积是V/N。剩余的体积（N-1）（V/N）被其他（N-1）个分子占据。教科书上的假设是，一个分子可以在一个瞬间到达体积V内的任何位置，这是错误的，导致吉布斯悖论。通过考虑单个分子的正确物理空间，获得了N-分子系统的配分函数，而不使用任何校正因子，从而产生系统的正确熵。因此，没有必要争论分子的相容性。两种理想气体混合的熵为零，无论是同种气体还是异种气体。通过对相空间的适当分配，系统的熵具有预期的广延性，从而消除了吉布斯佯谬。
英文摘要：
For an ideal gas consisting N molecules within a volume V, the volume accessible to each molecule at an instantaneous time is V/N. The rest of the volume, (N-1)(V/N), is occupied by other (N-1) molecules. The textbook assumption that a molecule can access any location inside the volume V at one instantaneous in time is wrong leading to the Gibbs paradox. By taking into account the correct physical space for individual molecules, the partition function for the N-molecule system is obtained without using any correction factor which gives rise to the correct entropy of the system. There is thus no need to argue about the distinguishability of molecules. Entropy of mixing two quantities of ideal gasses is zero no matter the gasses are the same type or different types. With the appropriate assignment of the phase space, the entropy of the system has the expected property of being extensive and the Gibbs paradox is removed.
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