ES 202 Fluid and Thermal Systems Lecture 17 More on properties and phases 1 21 2003 Road Map of Lecture 17 Continue exercise on property table water Common procedure in phase determination saturation table More on Compressed Liquid Approximation Practice with data interpolation linear bi linear Special models constant pressure process constant volume process Lecture 17 ES 202 Fluid Thermal Systems 2 What is the common starting point Review question In the procedure of phase determination of a substance what is the common starting point the saturation table It serves as a reference region which helps you to decide if you are in compressed subcooled liquid region two phase region superheated vapor region If the substance is in the two phase region the knowledge of quality mass fraction of vapor in the mixture is critical in completely identifying the state of the mixture Lecture 17 ES 202 Fluid Thermal Systems 3 More on Compressed Liquid Approximation As introduced yesterday the compressed liquid approximation can be expressed as u T P u f T v T P v f T weak function of T s T P s f T h T P u f T Pv f T h f T P Psat T v f T It can be interpreted as weak dependency of most properties on pressure in the compressed liquid region Hence most properties can be approximated by their saturated liquid values at the specified temperature Lecture 17 ES 202 Fluid Thermal Systems 4 Compressed Liquid Approximation on Phase Diagrams P v diagram T v diagram exact state con s Co ns ta nt p re ss ur el in e exact state tant t em p er atur e line approximate state approximate state Lecture 17 ES 202 Fluid Thermal Systems 5 Data Interpolation The property tables only tabulate discrete values for pressure or temperature as the independent property If you are interested in values which do not fall on the tabulated data points interpolation within the sandwich interval will be necessary Since the property tables report data at small intervals linear interpolation should be adequate for most purposes Example specify T not tabulated and x in two phase region If both independent intensive thermodynamic properties do not fall on the tabulated data points bi linear interpolation is necessary to completely specify the thermodynamic states Example specify P and T in superheated vapor region both not tabulated Lecture 17 ES 202 Fluid Thermal Systems 6 Constant Pressure Process Imagine a heating process in a cylinder with a constant weight as a lid closed system control mass Since pressure is constant you only need one more independent intensive property to specify the state Trace the process on P v diagram T v diagram Lecture 17 vapor liquid mixture of liquid and vapor heating Constant pressure line Constant pressure line ES 202 Fluid Thermal Systems 7 Constant Volume Process Imagine a heating process in a rigid enclosure closed system control mass vapor Since volume is constant specific volume is constant throughout the process Constant specific volume line liquid mixture of liquid and vapor heating Constant specific volume line Trace the process on a P v diagram T v diagram Lecture 17 ES 202 Fluid Thermal Systems 8