# A Third-Law Isentropic Analysis of a Simulated Hurricane

## TL;DR

This study demonstrates that using the third-law based potential temperature significantly alters isentropic analyses of a simulated hurricane, impacting entropy calculations, stream functions, and thermodynamic cycle assessments.

## Contribution

It introduces a third-law based potential temperature for moist air, showing its importance over traditional methods in hurricane analysis.

## Key findings

- Different moist-air potential temperatures lead to large discrepancies in isentropic plots.
- Third-law entropy provides more consistent and physically grounded analyses.
- Impacts include altered heat input, work, and efficiency calculations for hurricane cycles.

## Abstract

The moist-air entropy can be used to analyze and better understand the general circulation of the atmosphere or convective motions. Isentropic analyses are commonly based on studies of different equivalent potential temperatures, all of which are assumed to fully represent the entropy of moist air. It is, however, possible to rely either on statistical physics or the third law of thermodynamics when defining and computing the absolute entropy of moist air and to study the corresponding third-law potential temperature, which is different from the previous ones. The third law assumes that the entropy for the most stable crystalline state of all substances is zero when approaching absolute zero temperature. This paper shows that the way all these moist-air potential temperatures are defined has a large impact on: (i) the plotting of the isentropes for a simulation of the Hurricane DUMILE; (ii) the changes in moist-air entropy computed for a steam cycle defined for this Hurricane; (iii) the analyses of isentropic stream functions computed for this Hurricane; and (iv) the computations of the heat input, the work function, and the efficiency defined for this steam cycle. The moist-air entropy is a state function and the isentropic analyses must be completely determined by the local moist-air conditions. The large differences observed between the different formulations of moist-air entropy are interpreted as proof that the isentropic analyses of moist-air atmospheric motions must be achieved by using the third-law potential temperature defined from general thermodynamics.