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

2. 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. 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

4. 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

5. 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

6. 3.1 PVT Behavior of Pure Substances
Solid
Phase Pc
Liquid
Phase
triple
point
Gas
Vapor
Phase T Tc

7. 3.1 PVT Behavior of Pure Substances
Solid
Phase
Liquid
Phase Pc
triple
point
Gas
Vapor
Phase T Tc

8. 3.1 PVT Behavior of Pure Substances
PV diagram

9. 3.1 PVT Behavior of Pure Substances

10. Interactive Phase Diagram

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

12. 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

13. 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

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

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

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

17. 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

18. 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

19. 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