Presentation on theme: "Non-tabular approaches to calculating properties of real gases"— Presentation transcript:
1Non-tabular approaches to calculating properties of real gases
2The 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
3Properties 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.
4Departures 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
5The 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).
7Principle 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.
12Some 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.)
13Some 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
14Two-parameter equations of states Examples:Van der waalsDietericiRedlich KwongParameters (a, b) can be evaluated from critical point data usingVan der Waals: