NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.

Theoretical study on thermodynamic properties of NO gas

Nitric oxide(NO) is one of atmospheric molecules of interest and has attracted considerable attention due to its important role in the chemical process taking place in a flow field of hypersonic vehicle, in which the thermodynamic properties are required in the calculation of the aerothermodynamic flow field. Moreover, the total internal partition function is the key to calculating the thermodynamic properties of high-temperature gases. For diatomic molecules, according to the product approximation, the total internal partition function is split into three parts: electronic, vibration and rotation partition function. In this paper, by using the quantum statistical ensemble theory based on some classical thermodynamic and statistical formulae, the thermodynamic properties of NO are analyzed and discussed.Firstly, in order to obtain an accurate energy of molecule, the variational algebraic method(VAM) is employed to calculate the full vibrational energy, the resultis in good agreement with the experimental result and thus yielding the realistic predictions of the unobserved higher vibrational energy that converges to the dissociation limit. Secondly, an attempt is to use the full VAM vibrational energy, the Rydberg-Klein-Rees(RKR) vibrational energy, the simple Harmonic oscillator(SHO) model and the quantum-mechanical vibrational energy obtained by the multiconfiguration self-consistent-field(MCSCF) to calculate the vibrational partition function. Then, with the rotational contributions from the Müller-McDowell formula, the internal partition function can be determined by combining the product of electronic, vibration and rotation partition functions. Thirdly, according to the thermodynamic and statistical formulae, it is easy to calculate the internal energy, entropy and heat capacity for the NO molecule in a range of 1000-5000 K. Comparison of different calculated heat capacities with the experimental ones reveals the heat capacity, of which vibrational contributions determined by the full VAM vibrational energy accord better with the experimental ones, with the maximum relative error being no more than 2.4%, whereas it can be seen that those thermodynamic results evaluated from the SHO model attest to a failure for the summation of infinite vibrational energy. The thermodynamic results of NO may have proper applications in areas that can be of great importance in theoretical and(or) experimental aspects.