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* Reading Assignments:

* Reading Assignments:. 4.1 4.2 4.4 4.5 4.6 4.6.1 4.6.2. 5. Heterogeneous Systems. 5.1 Heterogeneous vs homogeneous. * Homogeneous systems:. Single phase – dry air. Thermal equilibrium and mechanical equilibrium. Closed system, two independent variables (e.g., T, p),

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* Reading Assignments:

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  1. * Reading Assignments: 4.1 4.2 4.4 4.5 4.6 4.6.1 4.6.2

  2. 5. Heterogeneous Systems 5.1 Heterogeneous vs homogeneous * Homogeneous systems: Single phase – dry air Thermal equilibrium and mechanical equilibrium Closed system, two independent variables (e.g., T, p), two thermodynamic degrees of freedom * Heterogeneous systems: More than one phase – dry air, water vapor, ice etc. Additional chemical equilibrium – no conversion of mass between one phase to another state variable? Open to exchanges between subsystems the degrees of freedom?

  3. Consider a two-component mixture, 1) Dry air 2) Water with two phases: water vapor and one condensate Let be a generic extensive variable (mass dependent), which can be any state variable we choose. The total system is described by contributions from the individual phase, The gas phase subsystem is specified by The condensate phase (a pure substance) is determined by are the molar abundances (number of moles) for dry air, water vapor and condensate, respectively.

  4. For a closed system, Assumptions: and because the amount of water vapor is very small in the system.

  5. In terms of molar properties, the change of for the total system where are the molar properties. In terms of specific properties, where are the specific properties.

  6. 5.2 Chemical Equilibrium Consider the Gibbs function for two-component system, By analogy, where is called the chemical potential (or the partial molar Gibbs function).

  7. For dT=0 and dp=0 phase transformation, The criterion for chemical equilibrium is for either or The flux of mass from one phase to another is exactly balanced by a flux in the reversed direction, i.e., the net diffusion of mass is zero.

  8. 5.3 Thermodynamic Degrees of Freedom • For dry air, Two independent properties (the equation of state) Two degrees of freedom • For a single component system (e.g., water substance) • with two phases (e.g., water vapor and cloud liquid water), Four independent properties Three equations from thermodynamic equilibrium of phases One degree of freedom

  9. For water substance with three phases (e.g., water vapor, • cloud liquid water, and cloud ice), Six independent properties Six equations Zero degree of freedom The Triple Point – the point at which vapor, water, and ice are at equilibrium at the same conditions (273.16K and 6.11mb).

  10. Gibbs’ Phase Rule: The number of degree of freedom is given by C: number of chemically distinct but nonreactive components P: number of phases

  11. 5.4 Characteristics of Water State space of pure water substance.

  12. 1) Above the critical point A homogeneous gas phase always No phase change 2) Below the critical point Heterogeneous state and phase changes allowed A zone of discontinuity where two phases coexist: vapor and liquid water; vapor and ice; ice and liquid water

  13. 3) Conditions for the coexistence of different phases at equilibrium Saturated phases: zero net flux of mass between phases Equilibrium Vapor Pressure with respect to water or ice 4) The triple point for water substance

  14. 5.5 Latent Heat The specific latent heat -- the heat absorbed by a system during an isobaric phase transition, The three latent heats are related by the latent heat of sublimation (solid vapor) the latent heat of fusion (solid liquid) the latent heat of evaporation (liquid vapor)

  15. How does latent heat change with temperature? Kirchhoff’s equation: For temperatures in the range of interest for meteorology only the latent heat of fusion has a significant variation.

  16. 5.6 Clausius-Clapeyron Equation How to relate the equilibrium vapor pressure to the temperature of the heterogeneous system? For water substance with two phases, the addition of chemical equilibrium results in a relationship between the equilibrium pressure and temperature, is the change of specific volume between the two phases, is the latent heat corresponds to the phase present.

  17. 1) Vapor and liquid phases is the equilibrium vapor pressure with respect to liquid water and is also called the saturated vapor pressure with respect to water. is the specific gas constant for water vapor.

  18. 2) Vapor and ice phases is the equilibrium vapor pressure with respect to ice and is also called the saturated vapor pressure with respect to ice. 3) Ice and liquid water phases

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  20. Problem: A certain cloud consists mostly of supercool water droplets at -10oC and maintains the ambient air at saturation with respect to liquid water at that temperature. Compute the equilibrium vapor pressure. If a ice particle spontaneously forms in the cloud, find out the associated equilibrium vapor pressure.

  21. Homework (4) 1. 0.2 kg and 0oC ice goes through some changes and becomes 100oC vapor under isobaric process, calculate the total heat required for the process. 2. Problem 2 3. Problem 3(a) 4. Problem 4(a)

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