论文标题
重新定义理想气体系统的相空间解决了吉布斯悖论
Redefining the Phase Space for Ideal Gas Systems Resolves the Gibbs Paradox
论文作者
论文摘要
对于体积V内的N分子组成的理想气体，瞬时分子可访问的体积为v/n。其余体积（N-1）（v/n）被其他（N-1）分子占据。教科书假设分子可以在一个瞬间瞬间访问V卷中的任何位置是错误的，导致Gibbs悖论。通过考虑到单个分子的正确物理空间，可以在不使用任何校正因子的情况下获得N-分子系统的分区函数，从而导致系统的正确熵。因此，无需争论分子的区分性。混合两次理想气体的熵是零，无论气体是相同类型或不同类型的熵。随着相空间的适当分配，系统的熵具有广泛的预期特性，并且去除了吉布斯悖论。
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.
