공정 열역학 Chapter 3. Volumetric Properties of Pure Fluids 고려대학교 화공생명공학과 강정원

Introduction Thermodynamic properties (U, H and thus Q, W) are calculated from PVT data PVT data are important for sizing vessels and pipelines Subjects PVT behavior of pure fluids Ideal gas behavior Real gas behavior Generalized correlation  when data are lacking

3.1 PVT Behavior of Pure Substances P-T diagram P critical point Solid Phase Super-critical (fluid) phase Pc Liquid Phase triple point Vapor Phase Gas T Tc

3.1 PVT Behavior of Pure Substances P-T diagram Component =1 Phase = 2 (V and L) F = 1 Vapor pressure at T1 vapor pressure curve Vaporization curve P Solid Phase Liquid Phase pvap Vapor Phase T T1

3.1 PVT Behavior of Pure Substances melting curve fusion curve P Solid Phase Liquid Phase Pc freezing pressure triple point Gas sublimation pressure Vapor Phase T Tc sublimation curve sublimation point freezing point

3.1 PVT Behavior of Pure Substances Solid Phase Pc Liquid Phase triple point Gas Vapor Phase T Tc

3.1 PVT Behavior of Pure Substances Solid Phase Liquid Phase Pc triple point Gas Vapor Phase T Tc

3.1 PVT Behavior of Pure Substances PV diagram

3.1 PVT Behavior of Pure Substances

Interactive Phase Diagram http://www.chm.davidson.edu/ChemistryApplets/PhaseChanges/PhaseDiagram.html

Single Phase Region Equation relating P, V, T  Equation of State Volume expansivity Isothermal compressibility

3.2 Virial Equation of State PVT behavior is complex  cannot be represented by simple equation Gas phase alone can be correlated with simple equation PV term is expanded as a function of P by a power series At low pressure, truncation after two terms usually provide satisfactory result

Ideal-Gas Temperature : Universal Gas Constant B’, C’, D’, ….  depends on component, temperature a  same for all species, function of temperature only PV H2 N2 Air O2 Useful for thermometry P

Ideal-Gas Temperature : Universal Gas Constant Ideal Gas Temperature Scale Make (PV)* proportional to T, (R: proportionality constant) Assign the value 273.16 K to triple point of water Kelvin scale temperature

Ideal-Gas Temperature : Universal Gas Constant Molecular volume becomes smaller Molecules are separated infinite distances Intermolecular forces approaches zero Universal Gas Constant

Two forms of the Virial Equation Compressibility B, B’ : the second virial coefficient C, C’ : the third virial coefficient Virial expression

Importance of the Virial Equation Many form of equation of state have been proposed Virial Equation has a firm basis in theory  Statistical mechanics B/V : interaction between two molecules (two-body interaction) C/V2 : three-body interaction

3.3 The Ideal Gas No interaction between molecules (B/V, C/V2 ,…=0) Internal energy of gases Real gas : function of T and P Ideal gas : function of T only Pressure dependency  resulting from intermolecular force There is no dependency in P The Equation of State Internal Energy Ideal gas

Implied Property Relations for an Ideal Gas Heat capacity at const. volume is a function of temperature only Enthalpy is also a function of temperature only Heat capacity at const. pressure is a function of temperature only Heat Capacity Relationship