1Lecture Ch. 4a• Equilibrium• Phase changes• Enthalpy changes from phase changes– Latent heat– Clapeyron equation– Clausius-Clapeyron equationCurry and Webster, Ch. 4 (pp. 96-115; skip 4.5, 4.6)For Tuesday: Homework Problem Ch.4 Prob. 5Curry and Webster, Ch. 4Quiz• Is water a polar molecule?• What is the Gibbs phase rule?• What is the relationship between twotemperatures at thermal equilibrium?• What is supercooled water?• What is the Clausius Clapeyron equation?Answer briefly and clearly, with appropriate equations or diagrams. Answers• Is water a polar molecule?• What is the Gibbs phase rule?2Answers• What is relationship between two temperatures atthermal equilibrium?• What is supercooled water?• What is the Clausius Clapeyron equation?Phase Diagrams• Pressure-temperature diagrams• Degrees of freedom• Pressure-volume diagramsPhase Equilibrium• Thermal equilibrium• Mechanical equilibrium• Chemical equilibrium3Degrees of Freedom ExampleName the five main components of the atmosphere. (a) If all components are in the gasphase, how many degrees of freedom are there in the system? (b) If water condenses orfreezes, does that number increase or decrease? (c) If new components are added bypollution, how does that change (i) the number of possible phases and (ii) the degrees offreedom of the atmosphere?Chemical Equilibrium• Two phases in equilibrium– Constant T, P• Phase changes– Constant T, P• (What was G?)€ ΔGT ,P= 0€ ΔGT ,P= 0Gibbs (Free) EnergyEntropy Change• Entropy for phase transition• Define latent heatClapeyron Equation• Enthalpy change for any phase transitionExact!(Not exact but usually good)Clausius-ClapeyronEquation• Latent heat of vaporization4Phase Change Relationships• Clapeyron equation– All phase changes– Non-ideal equations of state• Clausius-Clapeyron equation– Liquid-vapor equilibrium only: vL << vV– Ideal gas law for vapor: vV = RT/pClausius Clapeyron ExampleThe saturation vapor pressure at a temperature of 30°C is 42.4 hPa. The gas constant fordry air is 287 J K-1 kg-1. The gas constant for water vapor is 461 J K-1 kg-1.In addition to the constants given above, here is one more: the saturation vapor pressureat a temperature of 40°C is 73.8 hPa. Assuming that the latent heat of vaporization isconstant, use this information to calculate the numerical value for this latent heat.More Reminders• Virtual Temperature: The temperature air would have at the given pressure and density if therewere no water vapor in it• Potential Temperature: The temperature a parcel would have if it were brought adiabatically andreversibly to p0 (usually 1 atm)• Virtual Potential Temperature: The temperature a parcel would have if there were no water vaporin it (only condensed water) and if it were brought adiabatically and reversibly to p0 (usually 1 atm)• Equivalent Temperature: The temperature that an air parcel would have if all of the water vaporwere to condense in an adiabatic isobaric process• Equivalent Potential Temperature: The temperature a parcel would have if all of the water werecondensed in an adiabatic isobaric process and if it were brought adiabatically and reversibly to p0(usually 1 atm)Ch. 4: Problem 5Consider moist air at a temperature of 30°C, a pressure of 1,000 hPa, and a relativehumidity of 50%. Find the values of the following quantities:a) vapor pressureb) mixing ratioc) specific humidityd) specific heat at constant pressuree) virtual
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