Evaluating Thermodynamic PropertiesChapter 3

IntroductionPhaseIt is the quantity of matter that is homogenous in physical and chemical compositionPure SubstanceIt is the quantity of substance that is homogenous in chemical compositionExampleA system of water and water vapor is a Pure Substance existing in two phasesAir on the other hand, is not a pure substance, but is in a single phase

Deciding the stateState, as we know, is described by the propertiesSome of the properties are dependent on the othersAnd the state can be fixed by specifying just the independent propertiesFor simple compressible systems, like pure substances, and mixture of non reacting substances, State Principle says that the number of independent states is two

P-v-T relationPressure, P, Specific volume v, and the temperature T are the most important properties in thermodynamicsP, v and T can be obtained by direct measurementP-v-T surface is a 3-D graph of the three properties for a given substanceShown here are these for two different substances

P-v-T relationWater like substanceOther substance

P-v-T RelationBetween the single phase regions are the two phase regions where two phases exist in equilibrium, could be liquid-vapor, liquid-solid or even solid-vaporThe line between two phases is called the saturation lineAlong the line named triple line, all the three phases exist in equilibriumThe point where the two saturation lines meet is called the critical point

P-v-T RelationWe make the 3-D figure into a 2-D and easily understandable figure - called projectionsPhase diagram or the P-T diagramP-v DiagramT-v DiagramSaturation temperature is the temperature at which phase change occurs at a given pressureSaturation pressure is the pressure at which phase change occurs at a given temperature

Phase ChangeSub-cooled or compressed liquid refers to the liquid in the left part of the phase diagramThe part between the liquid and vapor state is the mixed stateThe right most part is the vapor state and also called the superheated vapor stateThe amount of vapor present in the mixed state is given by the quality of the mixtureIt is a property, and has a value of 0 in the liquid state and 1 in the vapor stateThe quality of the mixture is defined as

Phase ChangeThe most important phase changes considered in this class are the vaporization and condensationOther phases changes that occur are the melting-solidification and sublimation

Getting the Property ValuesThe properties are generally read from the tablesSaturated table gives the properties between the saturated lines (mixed zone)Super heated vapor table gives the properties in the super heated zone andThe sub cooled liquid table gives the properties in the sub cooled regionAs a function of temperature as well as pressure

Saturated Steam TablePressure BasedTemperature Based

Superheated and Sub cooled tables

EnthalpyThe term U+pV is used frequently in thermodynamicsThis is defined as the EnthalpyH=U+pV - Totalh=u+pv - specificUnits same as that of energy (Joules, kiloJoule etc)u =uf + x (ug uf)h = hf + x (hg hf) = hf + x hfgThe values in the tables are not measured directlyThey are measured as differences from a reference stateThese differ for substancesFor water it is 0.010C

Specific HeatsPressure p is constant, intensive propertySpecific volume v is constant, intensive propertySpecific Heat RatioUniversal Gas Constant

LiquidsIncompressible Substancev(T,p) ~ vf (T) - Specific Volumeu(T,p) ~ uf (T) - Internal Energyh(T,p) ~ uf (T) + p vf (T) ~ hf (T) + vf (T)[p psat(T)]If the term in red is very small then h(T,p) ~ hf (T) For an incompressible substance, cp = cv = cThis gives us u2-u1= c(T2-T1)h2-h1 = c (T2-T1) + v (p2-p1)

Ideal Gas LawThe concept of an ideal gas is a hypothetical idea, but it serves as a useful tool to explain the more complex real gas behavior. An ideal gas is a gas in which;the molecules occupy negligible volume,there is no interaction between the molecules,collisions between the molecules are purely elastic, implying no energy loss on collisionCompressible Substance

Ideal Gas ModelAt low pressures (< 400 psi) most gases exhibit an almost ideal behavior. The ideal gas law that applies to such gases can be studied as follows:PV = nRT

where P and T are the absolute pressure and temperature of the gas, n is the number of moles, and V is the volume occupied by the gas. R, the constant of proportionality, is called the universal gas constant.

Behavior of Real GasesIn general, gases do not exhibit ideal behavior. The reasons for the deviation from ideal behavior can be summarized as follows:Molecules for even a sparse system, such as gas, occupy a finite volume.Intermolecular forces are exerted between molecules.Molecular collisions are never perfectly elastic.Compressible SubstanceThe deviation from ideal behavior is greater for heavier gases because of the larger size of their molecules. Most gases compress more than ideal gas at low pressures, whereas the opposite is true at high pressures.

Compressible SubstanceIdeal gas

Real gas,

Compressibility Factor, to correct for non-ideality, the simplest equation of state uses a correction factor known as the gas compressibility factor,

Z=1 for Ideal Gases

Compressible SubstanceThe Z-factor can therefore be considered as being the ratio of the volume occupied by a real gas to the volume occupied by it under the same temperature and pressure conditions if it were ideal.The major limitation is that the gas deviation factor, Z, is not a constant but varies with changes in gas composition, temperature and pressure.

Compressible SubstanceIt must be determined experimentally. The results of experimental determinations of compressibility factors are presented graphically and usually take this form.This is the most widely used real gas equation of state.

Generalized compressibility chartGeneralized compressibility chart is drawn as Z v/s pR at const TR, where pR & TR are defined as pR = p/pc TR = T/Tc- pc = Critical Pressure- Tc = Critical Temperature

Ideal Gas ModelZ=1pv=RTpV=mRT

u=u(T)h=h(T) = u(T) +pv = u(T) + RT -- (1)Differentiate (1) wrt T,

cp(T) = cv(T) +R

Ideal Gas u, h, cp, cv For Constant specific heats ,

Polytropic ProcessIt is any quasiequilibrium process described byFor Ideal Gas

End Of Chapter 3

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