Presentation on theme: "Properties of pure substances"— Presentation transcript:
1 Properties of pure substances MEL140Properties of pure substances
2 Pure substanceA pure substance has the same chemical composition throughout.Are the following confined in a fixed volume pure substances:Ice (single component, single phase)A mixture of water and water vapor (single component, multiphase)Air in gas phase (multi-component, single phase)Oil in contact with water (multi-component single phase)A gaseous mixture containing N2,O2,H2O, CO2 obtained from burning kerosene (multicomponent, single phase)Liquid air in contact with gaseous air (multicomponent, multiphase) Objective: evaluating the properties for single component pure substances existing in one or more phases (multiphase).NYdegree C boiling point of nitrogen degree C boiling point of oxygenAlert: in chemistry a pure substance is defined such that it consists of onecomponent (chemical species) and therefore must be “non-mixture”. We follow adifferent definition (see above) in engineering thermodynamics.
3 PhasesA region within matter with distinct molecular arrangement that is homogeneousthroughout that region which is separated from other regions (if any) by distinct boundary surfaces. Physical properties (like density and refractive index) of each phase is different.The three principal phases:SolidLiquidGas
4 Phase equilibriumA system can be composed of subsystems with different molecular arrangements separated by phase boundaries (phases).Phase equilibrium prevails when no transfer of mass happens between phases.
5 The state postulateA property is characteristic of the system such as specific volume (v), temperature (T), pressure (P), (specific) internal energy (u).A state is the condition of a system as determined by its properties.A simple compressible system is a system whose only mode of performing quasi-equilibrium work is through a change of its volume against a pressure.The state postulate: The state of a simple compressible system consisting of a pure substance is completely specified by two independent intensive properties.The state postulate can be represented by an equation of state such as f(p,v,T)=0 (or say g(p,v,u)=0). It is often convenient to represent this functional relationship byA surface in p,v,T (or u,p,v) space or more commonly its projections on (p,v), (T,v) and (p,T) planes.Tables of properties
6 The P-v diagram Remove just enough heat to keep temperature constant as the volume is reduced.It will be observed that exceptduring 2-3, pressure also needs to be increased for executing this process in a quasi-equilibrium manner.During 1-2 you (notduring 2-3-4)321Shows isotherms onP-v diagram
7 The critical state: recapitulation At the critical state (Tc, Pc), saturated liquid and saturated vapor states are identical (SLL intersects SVL).Increasing/decreasing pressure at a given temperature leads to condensation/evaporation only if a state lies below the critical isotherm.
9 Critical properties of common fluids Water/steam:CP: 374o C (647.1 K), 22 Mpa (~more than 200 atm)at which specific volume m3/kg (~three times less dense STP)BP at atmospheric pressure ( kPa): 100o C (1 atm)Refrigerant 134a or R134a or 1,1,1,2-Tetrafluoroethane in your “freeze”:CP: 101o C, 4 Mpa (~40 atmosphere)BP at atmospheric pressure : -26o C, kPa (1 atm)Nitrogen:CP: -147o C, 3.4 MPaBP at atmospheric pressure : -196o CCarbon-dioxide:CP: 31.05oC ,7.39 Mpa (CO2 is not a “gas” in Delhi for six months, i.e. Apr-Sept)BP at atmospheric pressure: -78.5oCTable A.1 (Tc,Pc,vc)How far a state is away from critical point?Curious facts:Critical isotherm and the gas-vapor nomenclatureSupercritical fluidsT>Tcr and P>Pcr
10 Principle of corresponding states (van der Waal, 1880) Reduced temperature: Tr=T/TcReduced pressure: Pr=P/PcReduced volume: vr=v/vcRegardless of the substance, there is a universal equation of state connecting the reduced co-ordinates. So, thermodynamic states of different substances “correspond”.Can be stated as:“my equation of state has a universal form which can be identified by its predicted behavior at critical point”“Other equation of states might also be given similar universal forms by the same procedure”.
11 Principle of corresponding states (van der Waal, 1880, continued) Correspondence means the same reduced co-ordinates should mean the sameness of a third reduced property such as reduced volume.Compressibility factor is an important reduced property given by:Z signifies departure from ideal gas behavior. More discussion on significance in notes.Principle of corresponding states: All fluids when compared at the same Tr and Pr have the same Z and deviate from the ideal gas behavior to about the same degree.This principle is the basis of classifying systematizing organizing and compacting experimental measurements on P, V and T.
12 Critical compressibility of real gases Source:12
14 Some terminologyCompressed liquid or sub-cooled liquid: Liquid which is not about to vaporize (State 1)Saturated liquid: liquid which is about to vaporize (State 2)Saturated vapor: vapor which is about to condense (State 4)Saturated liquid-vapor mixture: a mixture of saturated liquid and saturated vapor (State 3)Superheated vapor: vapor that is not about to condense (State 5)
16 Latent heatThe energy absorbed by a system during a phase change process at a given pressure/temperature is called latent heat.Latent heat of fusion (melting)Latent heat of vaporization (boiling)Latent heat goes to change the molecular potential energy; in-fact temperature, a measure of molecular kinetic energy remains constant during a phase change process.
17 Saturation temperature, saturation pressure and saturation curve Phase change processes (e.g. “saturated liquid” boiling to “saturated vapor”) under a given pressure ( “saturation pressure” or Psat) take place at a given temperature( “saturation temperature” or Tsat).Therefore Psat=f (Tsat). A plot of this function is the saturation curveSaturation curve for water
18 Property diagram for phase change processes: the T-v diagram. 234Construct atdifferent pressures
19 The critical point The state (“point”) at which the saturated liquid andthe saturated vapor states areidentical.For water
20 The T-v diagram: saturated liquid line and the saturated vapor line Shows isobarson T-v diagramSaturated liquid and saturated vapor lines meet at the critical point.
21 The P-v diagram Remove weights to change pressure during 1-2, 4-5 (not Shows isotherms onP-v diagram
22 Extending the P-v diagram to include solid phase a solid at temperature lowerthan melting pointP-v diagram of asubstance whichcontracts onfreezing (mostexcept water)bb solid begins meltingcc solid completely melteddd liquid begins to vaporizeee liquid completely vaporized
23 Extending the P-v diagram to include solid phase a ice at -10oC, 1 atmbb ice begins melting(0oC), 1 atmSaturated liquid linesSaturatedsolid lineLIQUIDcc ice completely melted(0oC), 1 atmdd water begins to vaporize(100oC), 1 atmee water completelyvaporized (100oC), 1 atmSOLIDP-v diagram of asubstance whichexpands on freezing(e.g. water)
24 The triple lineThe states where all three phases co-exist in equilibrium lie on a straight line on the P-V or T-v diagram known as a triple line.All the “triple states” appear as a point on the p-T diagram and the corresponding (T,v) is called a “triple point”.Triple point of water: (0oC, 0.61 kPa)
26 The P-v-T surface For substances which For substances which contract on freezingFor substances whichexpand on freezing (such aswater).
27 Enthalpy: a combination property Enthalpy (h):h=u+pvEnthalpy is useful for studying processes (such as vaporization, heat transfer) taking place at constant pressure and processes that involve flow work
28 Objective Evaluate properties of states corresponding to: saturated liquid and saturated vaporsaturated liquid-vapor mixturessuperheated vaporcompressed/sub-cooled liquid
29 Saturated liquid and saturated vapor Subscript f represents “saturated liquid state”Subscript g represents “saturated vapor state”Subscript i represents saturated solid state.Propertyfg=Propertyg-Propertyfe.g. vfg =vg-vf represents volume change on vaporizationhfg = =hg-hf represents the “latent heat” or enthalpy of vaporization.SpecifiedFrom Table A-4
30 Saturated liquid and saturated vapor Saturated states lie on the curve f(Psat, Tsat)=0 and can therefore be specified by specifying either Psat, or TsatTable A-4 for water: (Psat,vf,vg,vfg,uf,ug,ufg,hf,hg,hfg,sf,sg,sfg) listed against TsatTable A-5 for water: (Tsat,vf,vg,vfg,uf,ug,ufg,hf,hg,hfg,sf,sg,sfg)listed against PsatSame data in Tables A-4 and A-5From Table A-4
31 Saturated liquid and saturated vapor Subscript f represents “saturated liquid state”Subscript g represents “saturated vapor state”Propertyfg=Propertyg-Propertyfe.g. vfg =vg-vf represents volume change on vaporizationhfg = =hg-hf represents the “latent heat” or enthalpy of vaporization (for vaporization under constant pressure)From Table A-4
32 Saturated liquid-vapor mixtures Refer to same Tables A-4 and A-5.The proportion of saturated vapor in the mixture is indicated by a new property “quality” or “dryness fraction”:The average value of a specific extensive property y (such as v,u,h) etc. for the mixture can be calculated from
33 Saturated liquid-vapor mixtures Refer to same Tables A-4 and A-5.The proportion of saturated vapor in the mixture is indicated by a new property “quality” or “dryness fraction”:x=0 for saturated liquid0<x<1 for saturated liquid-vapor mixturex=1 for saturated vaporx is undefined for compressed liquid and superheated vaporThe average value of a specific extensive property y (such as v,u,h) etc. for the mixture can be calculated from
34 Superheated vapor At least two properties need to be given to specify the state according to state postulateUsually either T or P and another property is given:At a superheated state:P<Psat @ given TT> PP/TP/TP/TVisit Table A-6 for water
35 Properties of pure substances (continued) MEL140
36 Compressed liquid At a compressed liquid state given Tgiven Pgiven P/Tgiven P/Tgiven P/TUsually compressed liquid tables are not available except Table A-7 for water at P> 0.5 MPa
37 Approximately evaluating properties at the compressed liquid state For a compressed liquid, properties are weakly dependent on p.Treat compressed liquid as a saturated liquid at the given temperature.Evaluate:h'hf?Usually better approximation for h is:h=u+pv'uf+pvf=hf-psatvf+pvf =hf+(p-psat)vf using v'vf and and hf=(uf+ psatvf).
38 Evaluate compressed liquid v at (T,p) At given T,v is notsensitiveto p.If no v is tabulated at given (P,T)find using saturation table (Table A.4 for water)
39 Determining the state (summary) Saturated liquid-vapormixture(A.4,A.5 for water)Compressed/subcooled liquid (A.7, A.4 if not A.7 for water)Superheated vapor(A.6 for water)P=Psat(T)TT=Tsat(P)Pvf<v<vguf<u<ughf<h<hgx=(y-yf)/yfg where y=v/u/h(0<x<1)x undefinedx undefined