Proof of the Nernst theorem

Abstract The Nernst heat theorem is proven from purely thermodynamic arguments connected with the second law of thermodynamics. The proof stipulates that $$T=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> is formalized by a Carnot thermometer, and is independent of the vanishing of the specific heats, or the unattainability of the zeroth isotherm. With this proof, the second law of thermodynamics would extend its applicability, and the third postulate of thermodynamics would be narrowed to the fact that the entropy of a finite density, chemically homogeneous body must not be negative.