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 Thermodynamics M. D. Eastin

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 Thermodynamics M. D. Eastin

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 Thermodynamics M. D. Eastin

Review of Systems Thus far we have worked exclusively with 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? of dry air, water vapor, and liquid/ice water? Dry Air Closed System p, T, V, m, Rd Thermodynamics M. D. Eastin

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 Thermodynamics M. D. Eastin

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

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

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 Thermodynamics M. D. Eastin

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

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 Water Vapor pv, Tv, Vv, mv, Rv Open sub-system Liquid Water pw, Tw, Vw, mw Thermodynamics M. D. Eastin

Water in Equilibrium pv, Tv pv, Tv pi, Ti pw, Tw 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 Thermodynamics M. D. Eastin

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 Thermodynamics M. D. Eastin

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 Thermodynamics M. D. Eastin

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 Thermodynamics M. D. Eastin

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” Thermodynamics M. D. Eastin

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 Sublimation Fusion Vaporization T C T (ºC) p (mb) 374 100 6.11 1013 221000 Liquid Vapor Solid Thermodynamics M. D. Eastin

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 Sublimation Fusion Vaporization T C T (ºC) p (mb) 374 100 6.11 1013 221000 Liquid Vapor Solid Thermodynamics M. D. Eastin

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: Sublimation Fusion Vaporization T C T (ºC) p (mb) 374 100 6.11 1013 221000 Liquid Vapor Solid Thermodynamics M. D. Eastin

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

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 C V P (mb) Vapor Solid Tt = 0ºC Liquid and Tc = 374ºC T1 6.11 221,000 T A B Thermodynamics M. D. Eastin

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 C V P (mb) Vapor Solid Tt = 0ºC Liquid and Tc = 374ºC T1 6.11 221,000 T B’ B Thermodynamics M. D. Eastin

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 C V P (mb) Vapor Solid Tt = 0ºC Liquid and Tc = 374ºC T1 6.11 221,000 T B’ B” Thermodynamics M. D. Eastin

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

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 Thermodynamics M. D. Eastin

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

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

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 p V 273K 373K dQ Thermodynamics M. D. Eastin

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

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 C V P (mb) Vapor Solid Tt Liquid Tc T1 T dQ Thermodynamics M. D. Eastin

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 C V P (mb) Vapor Solid Tt Liquid Tc T1 T L Thermodynamics M. D. Eastin

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

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

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

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 Thermodynamics M. D. Eastin

References Thermodynamics M. D. Eastin 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. Thermodynamics M. D. Eastin