What lies between a free adiabatic expansion and a quasi-static one?

TL;DR

The paper derives a new expression linking initial and final states in adiabatic processes, introducing a parameter that interpolates between free and quasi-static expansions, with practical approximations provided.

Contribution

It introduces a novel parameterized expression for adiabatic processes that bridges free and quasi-static expansions, including an approximate formula for practical evaluation.

Findings

Derived a relation connecting initial and final states in adiabatic processes.

Introduced a parameter r that interpolates between free and quasi-static expansions.

Provided an approximate expression for the parameter r.

Abstract

An expression is found that relates the initial and final volumes and temperatures for any adiabatic process. It is given in terms of a parameter r that smoothly interpolates between a free adiabatic expansion (r = 0) and a quasi-static one (r = 1). The parameter has to be evaluated numerically, but an approximate expression is given.