Heat and Gravitation. I. The Action Principle

TL;DR

This paper develops an action principle-based thermodynamic framework for ideal gases in gravitational fields, aiming to unify thermodynamics with gravity and lay groundwork for future extensions including radiation and relativity.

Contribution

It introduces a novel action principle formulation for thermodynamics in gravitational fields, connecting thermodynamics with gravitational theory and proposing new experimental tests.

Findings

Proposes a new approach to gas-radiation interaction.

Suggests the possibility of adiabatic equilibrium states.

Recommends centrifuge experiments to test gravitational effects on equilibrium.

Abstract

This first article of a series formulates the thermodynamics of ideal gases in a constant gravitational field in terms of an action principle that is closely integrated with thermodynamics. The theory, in its simplest form, does not deviate from standard practice, but it lays the foundations for a more systematic approach to the various extensions, such as the incorporation of radiation, the consideration of mixtures and the integration with General Relativity. We study the interaction between an ideal gas and the photon gas, and propose a new approach to this problem. We study the propagation of sound in a vertical, isothermal column and are led to suggest that the theory is incomplete, and to ask whether the true equilibrium state of an ideal gas may turn out be adiabatic, in which case the role of solar radiation is merely to compensate for the loss of energy by radiation into the cosmos. An experiment with a centrifuge is proposed, to determine the influence of gravitation on the equilibrium distribution with a very high degree of precision.