气体混合时的温度佯谬和自由能佯谬

THE TEMPERATURE PARADOX AND THE FREE ENERGY PARADOX AT GAS MIXING

本文从量子统计出发证明了:1.不同组元的弱简并量子理想气体在粒子质量差δ→0时,绝热混合后其温度T将有一突变的极值量,等温混合后自由能F也有一突变的极值量;2.当粒子热波长λ远小于粒子间的平均距离d时,此极值量与经典理想气体的热力学计算结果一致;3.温度佯谬和自由能佯谬本质上是由组元粒子数密度的突变所引起的,

Three Conclusions are deduced from Quantum statistical theory in this report: (1)If the mass difference δ between particles in idealgas with less-degenerate quantum states approaches zero there would be an extreme value of temperature in sudden change when the gases are adiabatelly mixed. The same tendance can be found in the case of free energy when they are mixed isothermally (2)The extreme value above is consistent with the result obtained by thermodynamic calculation for general ideal gas if the particle's wave-length λ is much less than the everage seperation between two particles (3)The temperature paradox and the free energy paradox can he ascrihed to sudden change of density of particles