Forms of the thermodynamic energy equation for moist air. (9th December 2018)

• Record Type: Journal Article
• Authors: Staniforth, Andrew; White, Andy
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 145:Number 718(2019)
• Page Start: 386
• Page End: 393
• Publication Date: 2018-12-09
• Subjects: dynamics -- Gibbs function -- ideal gas -- internal energy -- latent energy -- thermodynamic consistency -- thermodynamic equilibrium -- thermodynamic potential; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.3421
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract : The thermodynamic energy equation is derived in a self‐consistent manner for a mixture of dry air, water vapour and non‐precipitating liquid water. Gaseous components are assumed to be ideal gases, liquid water incompressible, and the mixture to be in thermodynamic equilibrium. Latent energy is treated as a component of internal energy. Various algebraically equivalent, but superficially different, forms are obtained and contrasted. Contrary to suggestions of an earlier study, a widely used form of the thermodynamic energy equation is shown to be legitimate. It neglects only the minute fractional volume occupied by liquid water, but is otherwise exact. Abstract : The thermodynamic energy equation is derived in a self‐consistent way for a mixture of dry air, water vapour and non‐precipitating liquid water. Various superficially different but algebraically equivalent forms are noted. A widely‐used almost exact form is shown to be a legitimate approximation.