Integral Inequalities in Thermodynamics

TL;DR

This paper derives and proves integral inequalities related to the Second Law of Thermodynamics, generalizing them to higher dimensions and demonstrating their use in generating other inequalities and establishing fundamental thermodynamic principles.

Contribution

It introduces a novel approach to deriving thermodynamic inequalities and extends their applicability to higher dimensions, linking them to key thermodynamic laws.

Findings

Derived integral inequalities from thermodynamic principles

Generalized inequalities to higher dimensions

Linked inequalities to the positivity of specific heats

Abstract

Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions with intended application of being used as a quick way of generating numerous other inequalities such as the Weighted Means Inequality. The proofs also serve as a way of establishing the equivalence of the Planck's statement of the Second Law and the positivity of specific heats.