In 2006, Zhu Ru-zeng published an article in this journal arguing that the zero limit of heat capacity at absolute zero cannot be derived from Nernst’s theorem; in 2024, an article published in this journal (2024, 43(6):3) opposed this conclusion, claiming that the Nernst’s theorem and the statement of vanishing of heat capacity at absolute zero are equivalent. This article demonstrates why Zhu Ru-zeng’s article is correct, and further discusses why the fact that heat capacity is zero as the temperature approaches zero cannot be used as a statement of the third law of thermodynamics.