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Phase of Water and Latent Heats

Phase of Water and Latent Heats. We must begin to account for the thermodynamics of water Our atmosphere contains dry air and water vapor Clouds contain dry air, water vapor, liquid water, and ice. Phase of Water and Latent Heats. Outline: Review of Systems

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Phase of Water and Latent Heats

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  1. Phase of Water and Latent Heats We must begin to account for the thermodynamics of water Our atmosphere contains dry air and water vapor Clouds contain dry air, water vapor, liquid water, and ice M. D. Eastin

  2. Phase of Water and Latent Heats • Outline: • Review of Systems • Thermodynamic Properties of Water • Multiple phases • Water in Equilibrium • Equilibrium Phase Changes • Amagat-Andrew Diagrams • Latent Heats for Equilibrium Phase Changes M. D. Eastin

  3. Review of Systems • Homogeneous Systems: • Comprised of a single component • Oxygen gas • Dry air • Water vapor • Each state variable (p, T, V, m) has • the same value at all locations • within the system M. D. Eastin

  4. Review of Systems • Thus far we have worked exclusively • a homogeneous (dry air only) closed • system (no mass exchange, but some • energy exchange) • So far, our versions of the Ideal gas law • and the first and second laws are only • applicable to dry air • What about water vapor? • What about the combination • of dry air and water vapor? • What about the combination • of dry air, water vapor, and • liquid/ice water? Dry Air Closed System p, T, V, m, Rd M. D. Eastin

  5. Review of Systems • Heterogeneous Systems: • Comprised of a single component • in multiple phases or multiple • components in multiple phases • Water (vapor, liquid, ice) • Each component or phase • must be defined by its own • set of state variables Water Vapor Pv, Tv, Vv, mv Ice Water Pi, Ti, Vi, mi Liquid Water Pw, Tw, Vw, mw M. D. Eastin

  6. Liquid Water pw, Tw, Vw, mw Open sub-system Dry Air (gas) p, T, V, md, Rd Closed sub-system Water Vapor pv, Tv, Vv, mv, Rv Open sub-system Ice Water pi, Ti, Vi, mi Open sub-system Energy Exchange Mass Exchange Review of Systems • Our atmosphere is a heterogeneous • closed system consisting of multiple • sub-systems • Very complex…we come back to it later M. D. Eastin

  7. Liquid Water pw, Tw, Vw, mw Open sub-system Dry Air (gas) p, T, V, md, Rd Closed sub-system Water Vapor pv, Tv, Vv, mv, Rv Open sub-system Ice Water pi, Ti, Vi, mi Open sub-system Energy Exchange Mass Exchange Review of Systems • For now, let’s focus our attention on • the one component heterogeneous • system “water” comprised of vapor • and oneother phase (liquid or ice) M. D. Eastin

  8. Thermodynamic Properties of Water • Single Gas Phase (Water Vapor): • Can be treated like an ideal gas when it • exists in the absence of liquid water or ice • (i.e. like a homogeneous closed system): pv = Partial pressure of water vapor (called vapor pressure) ρv = Density of water vapor (or vapor density) ( The mass of the H2O molecules ) ( per unit volume ) = mv/Vv Tv = Temperature of the water vapor Rv = Gas constant for water vapor ( Based on the mean molecular weights ) ( of the constituents in water vapor ) = 461 J / kg K M. D. Eastin

  9. Thermodynamic Properties of Water • Single Gas Phase (Water Vapor): • When onlywater vapor is present, we • can apply the first and second laws of • thermodynamics just like we did for • parcels of dry air M. D. Eastin

  10. Liquid Water pw, Tw, Vw, mw Open sub-system Water Vapor pv, Tv, Vv, mv, Rv Open sub-system Thermodynamic Properties of Water • Multiple Phases: • Can NOT be treated like an ideal gas • when water vapor co-exists with either • liquid water, ice, or both: • This is because the two sub-systems • can exchange mass between each • other when an equilibrium exists • This violates the Ideal Gas Law M. D. Eastin

  11. Water in Equilibrium • Multiple Phases: • When an equilibrium exists, the thermodynamic properties • of each phase are equal: Vapor and Liquid Vapor and Ice pv, Tv pv, Tv pi, Ti pw, Tw M. D. Eastin

  12. Water in Equilibrium • An Example: Saturation • Assume we have a parcel of dry air • located above liquid water • Closed system • Air is initially “unsaturated” • System is not at equilibrium Dry Air (no water) Liquid Water M. D. Eastin

  13. Water in Equilibrium • An Example: Saturation • After a short time… • Molecules in the liquid are in constant • motion (have kinetic energy) • The motions are “random”, so some • molecules are colliding with each other • Some molecules near the surface gain • velocity (or kinetic energy) through • collisions • Fast moving parcels (with a lot of • kinetic energy) leave the liquid water • at the top surface → vaporization M. D. Eastin

  14. Water in Equilibrium • An Example: Saturation • Soon there are a lot of water molecules • in the air (in vapor form)… • The water molecules in the air make • collisions as well • Some collisions result in slower moving • (or lower kinetic energy) molecules • The slower water molecules return to • the water surface → condensation M. D. Eastin

  15. Water in Equilibrium • An Example: Saturation • Eventually, the rate of condensation • equals the rate of evaporation • Rate of Rate of • Condensation = Evaporation • We have reached “Equilibrium” M. D. Eastin

  16. p (mb) C 221000 Liquid Fusion Vaporization Solid 1013 6.11 T Sublimation Vapor 0 100 374 T (ºC) Water in Equilibrium • Three Standard Equilibrium States: • Vaporization: Gas ↔ Liquid • Fusion: Liquid ↔ Ice • Sublimation: Gas ↔ Solid • Each of these equilibrium states • occur at certain temperatures • and pressures • Thus we can construct an • equilibrium phase change • graph for water M. D. Eastin

  17. p (mb) C 221000 Liquid Fusion Vaporization Solid 1013 6.11 T Sublimation Vapor 0 100 374 T (ºC) Water in Equilibrium • One Unique Equilibrium State: • It is possible for all three phases • to co-exist in an equilibrium at a • single temperature and pressure • Called the Triple Point M. D. Eastin

  18. p (mb) C 221000 Liquid Fusion Vaporization Solid 1013 6.11 T Sublimation Vapor 0 100 374 T (ºC) Water in Equilibrium • Critical Point: • Thermodynamic state in which • liquid and gas phases can • co-exist in equilibrium at the • highest possible temperature • Above this temperature, water • can NOT exist in the liquid phase • Other Atmospheric Gases: M. D. Eastin

  19. P (mb) Liquid C 221,000 Tc = 374ºC Vapor Liquid and Vapor T1 Solid T 6.11 Solid and Vapor Tt = 0ºC V Amagat-Andrews Diagram Equilibrium Phase Changes on P-V Diagrams: M. D. Eastin

  20. P (mb) Liquid C 221,000 Tc = 374ºC B Vapor A Liquid and Vapor T1 Solid T 6.11 Solid and Vapor Tt = 0ºC V Amagat-Andrews Diagram • Equilibrium Phase Changes on P-V Diagrams: • Vapor Phase (A→B) • Behaves like an ideal gas • Decrease in volume • Increase in pressure • Heat Removed M. D. Eastin

  21. P (mb) Liquid C 221,000 Tc = 374ºC B’ B Vapor Liquid and Vapor T1 Solid T 6.11 Solid and Vapor Tt = 0ºC V Amagat-Andrews Diagram • Equilibrium Phase Changes on P-V Diagrams: • Liquid and Vapor Phase (B→B’) • Small change in • volume causes • condensation • Some liquid water • begins to form • No longer behaves like • an ideal gas M. D. Eastin

  22. P (mb) Liquid C 221,000 Tc = 374ºC B” B’ Vapor Liquid and Vapor T1 Solid T 6.11 Solid and Vapor Tt = 0ºC V Amagat-Andrews Diagram • Equilibrium Phase Changes on P-V Diagrams: • Liquid and Vapor Phase (B’→B”) • Condensation occurs due • to a decrease in volume • Constant temperature • Constant pressure • Water vapor pressure • is at equilibrium M. D. Eastin

  23. P (mb) Liquid C 221,000 Tc = 374ºC B” Vapor C Liquid and Vapor T1 Solid T 6.11 Solid and Vapor Tt = 0ºC V Amagat-Andrews Diagram • Equilibrium Phase Changes on P-V Diagrams: • Liquid and Vapor Phase (B”→C) • All the vapor has condensed • into liquid water M. D. Eastin

  24. Amagat-Andrews Diagram • Equilibrium Phase Changes on P-V Diagrams: • Liquid Phase (C→D) • Small changes in volume • produce large increases • in pressure • Liquid water is virtually • incompressible P (mb) Liquid C 221,000 D Tc = 374ºC Vapor C Liquid and Vapor T1 Solid T 6.11 Solid and Vapor Tt = 0ºC V M. D. Eastin

  25. P (mb) Liquid C 221,000 Tc = 374ºC Vapor T1 Solid T 6.11 Tt = 0ºC V Amagat-Andrews Diagram • Equilibrium Phase-Change Range: • The range of volumes for • which equilibrium occurs • decreases with increasing • temperature M. D. Eastin

  26. P (mb) Liquid C 221,000 Tc = 374ºC Vapor Liquid and Vapor T1 Solid T 6.11 Solid and Vapor Tt = 0ºC V Amagat-Andrews Diagram • Critical Point: • Maximum temperature • at which condensation • (or vaporization) can • occur • Water vapor obeys the • Ideal Gas Law at • higher temperatures M. D. Eastin

  27. 273K 373K p dQ V Latent Heats during Phase Changes • Homogeneous System: • Vapor only • Behaves like Ideal Gas • Isobaric Process • Heat (dQ) added or removed • from the system • Temperature changes • Volume changes M. D. Eastin

  28. P (mb) Liquid C Tc dQ Vapor dQ T1 Solid T dQ Tt V Latent Heats during Phase Changes • Heterogeneous System: • Liquid and Vapor • Isobaric Process • Heat (dQ) added or removed • from the system • Temperature constant • Volume changes M. D. Eastin

  29. P (mb) Liquid C Tc dQ Vapor dQ T1 Solid T dQ Tt V Latent Heats during Phase Changes • Definition of Latent Heat (L): • Heat absorbed (or given away) • during an isobaric and isothermal • phase change • The heat is needed to form (or • (results from the breaking of) • the molecular bonds that hold • water molecules together M. D. Eastin

  30. P (mb) Liquid C Tc L Vapor L T1 Solid T L Tt V Latent Heats during Phase Changes • Definition of Latent Heat (L): • Heat absorbed (or given away) • during an isobaric and isothermal • phase change • Magnitude varies with temperature • However, the range of variation • is very small for the range of • pressures and temperatures • observed in the troposphere • Assumed constant in practice M. D. Eastin

  31. Vaporization Condensation (Lv or lv) Sublimation (Ls or ls) Gas Solid Liquid Fusion (Lf or lf) Latent Heats during Phase Changes The Different Latent Heats: Values for lv, lf, and ls are given in Table A.3 of the Appendix as a function of temperature M. D. Eastin

  32. Gas Solid Liquid Latent Heats during Phase Changes Heat is Absorbed (dQ > 0): Vaporization Condensation (Lv or lv) Sublimation (Ls or ls) Fusion (Lf or lf) M. D. Eastin

  33. Gas Solid Liquid Latent Heats during Phase Changes Heat is Released (dQ < 0): Vaporization Condensation (Lv or lv) Sublimation (Ls or ls) Fusion (Lf or lf) M. D. Eastin

  34. Phase of Water and Latent Heats • Summary: • Review of Systems • Thermodynamic Properties of Water • Multiple phases • Water in Equilibrium • Equilibrium Phase Changes • Amagat-Andrew Diagrams • Latent Heats for Equilibrium Phase Changes M. D. Eastin

  35. References Petty, G. W., 2008: A First Course in Atmospheric Thermodynamics, Sundog Publishing, 336 pp. Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics, Cambridge Press, 197 pp. Wallace, J. M., and P. V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467 pp. M. D. Eastin

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