重力场中理想气体的垂直“P-V”循环：两种气体密度分布模型的比较

重力场中密闭于刚性容器中的理想气体在垂直方向上反复压缩和膨胀可形成“压力一体积”（P—V）循环。如果气体工作在两个不同温度的热源之间，此循环可实现“热一功”转化。有别于“卡诺循环”，此垂直方向上的循环的“热一功”转化效率的计算必须给出气体在重力场中的密度分布方式，即“热一一功”转化效率与气体的密度分布方式有关。这一结论表明：重力场中气体的可逆循环效率与工质的性质有关。采用玻尔兹曼气体密度分布模型计算此循环的熵变，结果符合热力学第二定律。但在采用修正的有上边界的气体密度分布模型计算时，结果违背热力学第二定律。作者认为：根据能量守恒定律，重力场中气体密度分布应该有上边界。并指出，采用任何重力场中有上边界的气体密度分布模型均会导致违背热力学第二定律的计算结果。本文的计算表明热力学第二定律可能存在的局限性。

In gravitational field, the vertically expanding and compressing of the ideal gas could create a （P-V） cycle process to convert heat energy into mechanical one as long as the gas substance work between two hot reserviors of different temperature. However the heat-mechanical energy converting efficiency in such vertically P-V cycle can not be calculated without the density distribution of the gas in gravitational field,unlike that in Carnot-efficiency Cycle in wich the heat-mechanical efficiency depends only on the temperatures of the two hot reserviors. Namely the heat-mechanical energy converting efficiency in such vertically P-V cycle would depend on the characteristic of the working gas substance. With the Boltzmann＇s distribution for calcualation of the cyclic entropy, the result is consistent with Second Law of Thermodynamics. However, if the gas distribution had a top boundary in gravitational field, the calculation results would contradict to Second Law of Thermodynamics. The author consider that the gas distribution should have a top boundary in gravitational field in terms of the energy conservation law. Furthermore,the author propose that if the gas with a top boundary in gravitational field Was adopted, whatever the distribution mathematic modle might be, the calcualation of the cyclic entropy would lead to a result contravening to Second Law of Thermodynamics. Therefore the analysis in this article reveals that the second law of thermodynamics is not universal.