Thermo I - Chapter 3. Volumetric Properties of Pure Fluids...

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Unformatted text preview: Chapter 3. Volumetric Properties of Pure Fluids The mathematic equation of PVT is called equation of state. The most simple equation of state is PV = RT, which can be used for ideal gas. PVT BEHAVIOR OF PURE SUBSTANCES Diagram for a pure substance The three lines display conditions of P and T at which two phases may coexist, and divided the diagram into single-phase regions. The subcooled-liquid and the superheated-vapor regions Isotherms in the subcooled-liquid regions are steep because liquid volumes change little with large change in pressure The lines: two-phase coexist region The critical point The triple point: T=273.16K P=0.0061 bar At point 2 (triple point), according to the phase rule F = 2 - + N=2-3+1=0 The points at any of the two-phase lines, F = 1. PVT Diagram An equation of state may be solved for any one of the three quantities P, V, or T as a function of the other two. Example: For incompressible fluid, both and are zero. For liquids is almost positive (liquid water between 0C and 4C is an exception), and is necessarily positive. At conditions not close to the critical point, and can be assumed constant: ) ( ) ( ln 1 2 1 2 1 2 P P T T V V--- = VIRIAL EQUATIONS OF STATE For gases and vapors, the curve of CD in Figure 3.2(b) shows V decreases as P increases in a relatively simple way, which can be described by PV = a(1+ BP+ CP 2 + DP 3 + ) (3.6) (at constant temperature) where a, B, C, etc., are constants for a given temperature and a given chemical species. At low pressure, PV = a(1+ BP+ CP 2 ) is good enough A plot of PV vs. P for four gases at 271.16K (triple point of water) The limiting value of PV as P 0 is written as (PV)* Assigns the value 273.16 K to the temperature (triple point of water and denoted by subscript t): where P 0, the volume of the fraction of molecules to the total volume occupied by the gas and the attraction force between molecules become negligible. These conditions define an ideal-gas state.. The constant R is called the universal gas constant. From figure 3.4 we have (PV) t * = 22,711.8cm 3 bar mol-1 So Two Forms of the Virial Equation A useful auxiliary thermodynamic property is defined by the equation: Both (3.11) and (3.12) called virial expansion B, C, D B, C, D are virial coefficients, they are related by Another alternative equation using V instead of P The Ideal Gas The B/V is mainly from two molecular interaction, and C/V 2 is from three molecular interaction , etc. The high order of Virial Coefficients decreases rapidly. This means that C V is only the function of T for ideal gas For ideal gas, from the definition of C V Same for H. For ideal gases H= U + PV = U(T) + RT = H(T) (3.17) For ideal gas, , H also is a function of temperature only C P is a function of temperature only C p and C v are not constant, but they vary with temperature in the same way This relationship can be applied to ideal gas only....
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Thermo I - Chapter 3. Volumetric Properties of Pure Fluids...

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