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Thermo I

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

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Chapter 3. Volumetric Properties of Pure Fluids

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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 - π + N=2-3+1=0 The points at any of the two-phase lines, F = 1.
PVT Diagram

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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 β andκ are zero. For liquids β is almost positive (liquid water between 0°C and 4°C is an exception), and κ is necessarily positive. At conditions not close to the critical point, β andκ can be assumed constant: ) ( ) ( ln 1 2 1 2 1 2 P P T T V V - - - = κ β
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+ B’P+ C’P 2 + D’P 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+ B’P+ C’P 2 ) is good enough A plot of PV vs. P for four gases at 271.16K (triple point of water)

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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

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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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