本文采用几种不同的方法严格地证明热容量表述与能斯特表述是可相互推导的、是等效的. 应用这两种表述取代一百多年来出现在教科书中的能斯特定理和/或绝对零度不能达到原理，成为热力学第三定律的创新表述，可确保热力学第三定律是客观世界的真实反映，从而完善经典热力学理论体系.

Several different methods are used to prove strictly that the heat capacity statement and the Nernst statement are mutually derivable and equivalent. The application of the two statements to replace the Nernst theorem and/or the unattainability principle of absolute zero temperature, which have appeared in textbooks for more than one hundred years, as the innovative statements of the third law of thermodynamics can ensure that the third law of thermodynamics is a true reflection of the objective world, thus improving the theoretical system of classical thermodynamics.