Reconstructing adiabats

TL;DR

This paper presents a method to derive the equations of state for thermodynamic substances using isotherms and adiabats, involving complex calculations that often need numerical solutions.

Contribution

It introduces an explicit approach to reconstruct thermodynamic equations of state from limited thermodynamic data, including both calibrated and uncalibrated cases.

Findings

Explicit formulas for entropy functions in simple examples

Method involves solving non-linear equations and numerical integration

Applicable to both calibrated and uncalibrated thermodynamic systems

Abstract

We give an explicit method for calculating the equations of state of a thermodynamical substance from the following information: in the calibrated case, the system of isotherms and a single adiabat, in the uncalibrated one, the same but with two adiabats. For simple examples the entropy function can be computed explicitly from this material but it involves steps (solution of non-linear equations and an integration) which will usually require numerical methods for their implementation.