Presentation on theme: "Non-tabular approaches to calculating properties of real gases"— Presentation transcript:
1 Non-tabular approaches to calculating properties of real gases
2 The critical stateAt the critical state (Tc, Pc), properties of saturated liquid and saturated vapor are identicalif a gas can be liquefied at constant T by application of pressure, T·Tc.if a gas can be liquefied at constant P by reduction of T, then P·Pc.the vapor phase is indistinguishable from liquid phase
3 Properties of the critical isotherm The SLL and SVL intersect on a P-v diagram to form a maxima at the critical point.On a P-v diagram, the critical isotherm has a horizontal point of inflexion.
4 Departures from ideal gas and the compressibility factor For an ideal gasOne way of quantifying departure from ideal gas behavior to evaluate the “compressibility factor” (Z) for a true gas:Both Z<1 and Z>1 is possible for true gases
5 The critical state and ideal gas behavior At the critical state, the gas is about to liquefy, and has a small specific volume.is very large Z factor can depart significantlyfrom 1.Whether a gas follows ideal gas is closelyrelated to how far its state (P,T) departsfrom the critical state (Pc, ,Tc).
7 Principle of corresponding states (van der Waal, 1880) Reduced temperature: Tr=T/TcrReduced pressure: Pr=P/PcrCompressibility factor:Principle of corresponding states: All fluids when compared at the same Tr and Pr have the same Z and all deviate from the ideal gas behavior to about the same degree.
12 Some desirable characteristics of equations of state Adjustments to ideal gas behavior shoujd have a molecular basis (consistency with kinetic theory and statistical mechanics).Pressure increase leads to compression at constant temperatureCritical isotherm has a horizontal point of inflection:Compressibility factor (esp. at critical state consistent with experiments on real gases.)
13 Some equation of states Two-parameter equations of stateVirial equation of statesZ=1+A(T)/v+B(T)/v2+…. (coefficients canbe determined from statistical mechanics)Multi-parameter equations of state with empirically determined coefficients:Beattie-BridgemanBenedict-Webb-Rubin Equation of StateOftenbasedon theory
14 Two-parameter equations of states Examples:Van der waalsDietericiRedlich KwongParameters (a, b) can be evaluated from critical point data usingVan der Waals: