Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic thermodynamic concepts
- 2 Budget equations
- 3 The first law of thermodynamics
- 4 The second law of thermodynamics
- 5 Thermal radiation
- 6 Thermodynamic potentials, identities and stability
- 7 The constitutive equations for irreversible fluxes
- 8 State functions of ideal gases
- 9 State functions of the condensed pure phase
- 10 State functions for cloud air
- 11 Heat equation and special adiabatic systems
- 12 Special adiabats of homogeneous systems
- 13 Thermodynamic diagrams
- 14 Atmospheric statics
- Answers to problems
- List of frequently used symbols
- List of constants
- References and bibliography
- Index
9 - State functions of the condensed pure phase
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Basic thermodynamic concepts
- 2 Budget equations
- 3 The first law of thermodynamics
- 4 The second law of thermodynamics
- 5 Thermal radiation
- 6 Thermodynamic potentials, identities and stability
- 7 The constitutive equations for irreversible fluxes
- 8 State functions of ideal gases
- 9 State functions of the condensed pure phase
- 10 State functions for cloud air
- 11 Heat equation and special adiabatic systems
- 12 Special adiabats of homogeneous systems
- 13 Thermodynamic diagrams
- 14 Atmospheric statics
- Answers to problems
- List of frequently used symbols
- List of constants
- References and bibliography
- Index
Summary
The purpose of this chapter is to derive expressions for the specific partial quantities ψk = vk, Sk, ek, hk, fk, μk, k = 2, 3 for the condensed phases of water vapor. These quantities are needed to describe the thermodynamics of cloud air. In our treatment we assume that the liquid water and ice occur unmixed and neither liquid water nor ice contain foreign materials. Due to this assumption we cannot describe the formation of a water droplet. Such a droplet forms when water vapor condenses on a suitable aerosol particle so that the resulting droplet cannot be viewed as a pure substance. With this in mind, we may consider the ψk as the pure phase, i.e.. For simplicity we leave out the superscript ∘ denoting the pure phase and also drop the suffix k since confusion is unlikely. In the final section we will add the suffix k for completeness and accuracy.
The material coefficients
First of all, we need to define the coefficients of the isothermal compressibility (K) and the adiabatic compressibility (?S). They are defined by
Similarly, we define the isochoric pressure coefficient β and the isobaric expansion coefficient v* by
The quantities ?, β and v* are not independent. We recognize this by writing the state equation according to the Appendix of Chapter 6 in the form
Expansion of (9.5) gives
This expression is also valid if we choose any of the independent variables T, v and p as constant.
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- Thermodynamics of the AtmosphereA Course in Theoretical Meteorology, pp. 137 - 143Publisher: Cambridge University PressPrint publication year: 2004