The reversible adiabatic equation for ideal gas (T \({\text{V}}_{\text{m}}^{\gamma{-1}}\) = C) is one of the most important equations in thermodynamics. But there is still a lack of theoretical explanation of the constant C at present. Since the reversible adiabatic process is isentropic process, the constant C could be expressed as a function of entropy through the statistical thermodynamic method. According to the different heat capacities and heat capacity ratios, the molecules of ideal gas are divided into three sorts that are monatomic molecules, linear polyatomic molecules (which include the diatomic molecules) and nonlinear polyatomic molecules. Although the calculation formulas for entropy of different kinds of molecules are very different, their expressions of constant C are similar. All of them could be expressed as C = N × exp(S_m/C_V,m), where N is structure parameter. The reversible adiabatic equation was extended to a more general equation T \({\text{V}}_{\text{m}}^{\gamma-1}\) = N × exp(S_m/C_V,m), which could be applied to any process for ideal gas.

理想气体的可逆绝热方程（T \({\text{V}}_{\text{m}}^{\gamma{-1}}\) = C）是热力学中最重要的方程之一。但目前对常数C仍缺乏理论解释。由于可逆绝热过程是等熵过程，常数C可以通过统计热力学方法表示为熵的函数。根据热容和热容比的不同，理想气体分子分为单原子分子、线性多原子分子（包括双原子分子）和非线性多原子分子三种。虽然不同种类分子熵的计算公式有很大差异，但它们对常数C的表达是相似的。它们都可以表示为C  =  N  × exp( S _m / C _{V ,m} )，其中N是结构参数。可逆绝热方程扩展为更一般的方程T \({\text{V}}_{\text{m}}^{\gamma-1}\) = N  × exp( S _m / C _{V ,m} )，可应用于任何理想气体过程。