克劳修斯熵表达式适用于实际气体的分子动力学验证

Verification of Clausius entropy expression for real gases based on molecular dynamics

克劳修斯熵是热力学的核心概念.然而,克劳修斯熵表达式的引入是基于理想气体假定的,因此有必要论证克劳修斯熵表达式在实际气体中的适用性.通过回顾,我们发现已有的证明方法都是需借助两种工质循环的间接论证.本文通过分子动力学模拟了氩工质和二氧化碳工质在不同高压下的加热过程和可逆热力学循环,直接验证了克劳修斯熵表达式在实际气体中的适用性.在验证过程中发现,正是由于实际气体热力学过程中存在分子动能和势能之间的转换,才导致其热力学参数间的关系不同于理想气体,但是由于这种转化发生在系统的内部,克劳修斯熵表达式是不变的.

Clausius entropy is a core concept of thermodynamics.The derivation of the Clausius entropy expression is based on the assumption of an ideal gas,so it is necessary to verify the adaptability of the Clausius entropy expression in the real gas.Although the theoretical method can prove that the Clausius entropy expression is equally applicable to any real gas,there are still some shortcomings.For example,it needs to be proved by the circulation of the ideal gas with the real gas,rather than by the entropy change of the thermodynamic process,and the microphysical mechanisms of the thermodynamic parameter relationships of the real gas that differ from those of the ideal gas cannot be analyzed.However,most extant literature or textbooks do not explain this and instead apply the expression of entropy based on the assumption of an ideal gas to the real gas,which is insufficiently rigorous.Therefore,it is necessary to apply molecular dynamics simulation to provide a direct proof of Clausius entropy expression by simulating the thermodynamic processes of real gases.Firstly,the temperature,pressure,and density obtained from simulations during the isothermal process are compared with data from the National Institute of Standards and Technology(NIST)to verify the accuracy of the molecular dynamics simulation under high pressures.The isothermal processes of argon and carbon dioxide at high pressures are simulated,and the relative errors are within 8%compared with the NIST data,thus demonstrating the accuracy of the calculations.In addition,the reversibility of the simulated process is verified in this work by comparing the thermodynamic results of the adiabatic compression process with those of the isentropic process,and when the input work at each step of the adiabatic compression process is small enough,the calculated results are very close to the isentropic line,which indicates that the thermodynamic process of simulation is approximately reversible.Thirdly,the heat temperature quotients of isochoric process are calculated,and the results are compared with the corresponding entropy changes in the NIST(the relative errors are less than 5%),thus directly verifying the applicability of the Clausius entropy expression to real gases.Then,the thermodynamic cycles of argon and carbon dioxide under high pressures are simulated to further check whether the Clausius entropy expression is relevant to the real gas by modeling whether the sum of heat and temperature quotients of the thermal cycle process is zero.The results show that the sum of the heat temperature quotients of the cycles is extremely small,which further verifies that the Clausius entropy expression is also applicable to the real gas.Finally,the microscopic analysis indicates that the relationship of thermodynamic parameters in real gas thermodynamic processes differs from the physical mechanism of an ideal gas because of the interconversion of molecular kinetic energy and molecular potential energy.Obviously,when the system pressure is small,the conversion between molecular kinetic energy and molecular potential energy inside the ideal gas system is small,and the variation of heat capacity is negligible;when the system pressure increases,the conversion between molecular kinetic energy and molecular potential energy inside the system increases,and the variation of heat capacity increases accordingly.Since this interconversion occurs within the system,the Clausius entropy expression remains unchanged.