Tarik Al-Shemmeri. Engineering Thermodynamics (776123), страница 2
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General DefinitionsEngineering Thermodynamics••••••PCR = 22.09 MPaTCR = 374.14 oC (or 647.3 oK)vCR = 0.003155 m3/kguf = ug =2014 kJ/kghf =hg = 2084 kJ/kgsf = sg =4.406 kJ/kgK1.4 Thermodynamic ProcessesA process is a path in which the state of the system change and some properties vary from theiroriginal values. There are six types of Processes associated with Thermodynamics:Adiabatic : no heat transfer from or to the fluidIsothermal : no change in temperature of the fluidIsobaric : no change in pressure of the fluidIsochoric : no change in volume of the fluidIsentropic : no change of entropy of the fluidIsenthalpic : no change of enthalpy of the fluidDownload free ebooks at bookboon.com102.
Thermodynamics working fluidsEngineering Thermodynamics2. Thermodynamics working fluidsBehaviour of the working substance is very essential factor in understanding thermodynamics. Inthis book, focus is given to pure substances such as gases and steam properties and how they areinterrelated are important in the design and operation of thermal systems.The ideal gas equation is very well known approximation in relating thermal properties for a statepoint, or during a process.
However, not all gases are perfect, and even the same gas, may behaveas an ideal gas under certain circumstances, then changes into non-ideal, or real, under differentconditions. There are other equations, or procedures to deal with such conditions. Steam or watervapour is not governed by simple equations but properties of water and steam are found in steamtables or charts.2.1 The Ideal GasIdeally, the behaviour of air is characterised by its mass, the volume it occupies, its temperature andthe pressure condition in which it is kept. An ideal gas is governed by the perfect gas equation ofstate which relates the state pressure, volume and temperature of a fixed mass (m is constant) of agiven gas ( R is constant ) as:PV= mRTWhere(1)P – Pressure (Pa)V – Volume (m3)T – Absolute Temperature (K)T(K) = 273 + t ( C )m – mass (kg)R – gas constant (J/kgK)The equation of state can be written in the following forms, depending on what is needed to becalculated1.
In terms of the pressure2. In terms of the volume3. In terms of the mass4. In terms of the temperaturemRTVmRTV=PPVm=RTPVT=mRP=(2)(3)(4)(5)Download free ebooks at bookboon.com112. Thermodynamics working fluidsEngineering Thermodynamics5. In terms of the gas constant6. In terms of the densityPVmTmPρ= =V RTR=(6)(7)The specific gas constant R, is a property related to the molar mass (M) in kg/kmol, of the gas andthe Universal gas constant Ro asR = Ro / M(8)where Ro = 8314.3 J/kgKThe ideal gas equation can also be written on time basis, relating the mass flow rate (kg/s) and thevolumetric flow rate (m3/s) as follows:P Vt = mt R T(9)Please click the advertdongenergy.com/jobAmbitiousand curious?We are looking for young andhighly educated engineersand finance students.Join us at dongenergy.com/jobDownload free ebooks at bookboon.com122.
Thermodynamics working fluidsEngineering Thermodynamics2.2 Alternative Gas Equation During A Change Of State:The equation of state can be used to determine the behaviour of the gas during a process, i.e. whathappens to its temperature, volume and pressure if any one property is changed. This is defined bya simple expression relating the initial and final states such as :P1V1 P2V2=T1T2(10)this can be rewritten in terms of the final condition, hence the following equations are geerated :Final PressureP2 = P1 xT2 V1xT1 V2(11)Final TemperatureT2 = T1 xP2 V2xP1 V1(12)Final VolumeV2 = V1 xP1 T2xP2 T1(13)2.3 Thermodynamic Processes for gasesThere are four distinct processes which may be undertaken by a gas (see Figure 2.1):a) Constant volume process, known as isochoric process; given by:-P1 P2=T1 T2(14)b) Constant pressure process; known as isobaric process, given by:-V1 V2=T1 T2(15)c) Constant temperature process, known as isothermal process, given by:-P1V1 = P2V2(16)d) Polytropic process given by:-Download free ebooks at bookboon.com132.
Thermodynamics working fluidsEngineering ThermodynamicsnP1V1 = P2V2n(17)Note when n = Cp/Cv, the process is known as adiabatic process.PressurereisobaricisochoricisothermaladiabaticVolumeFigure 2.1: Process paths2.4 Van der Waals gas Equation of state for gasesThe perfect gas equation derived above assumed that the gas particles do not interact or collidewith each other. In fact, this is not true. The simpliest of the equations to try to treat real gases wasdeveloped by Johannes van der Waals. Based on experiments on pure gases in his laboratory, vander Waals recognized that the variation of each gas from ideal behavior could be treated byintroducing two additional terms into the ideal gas equation.
These terms account for the fact thatreal gas particles have some finite volume, and that they also have some measurable intermolecularforce. The two equations are presented below:PV = mRTP=RTa− 2v −b v(18)where v is the specific volume ( V/m ), and the Numerical values of a & b can be calculated asfollows:27 ⋅ R ⋅ Ta=64 ⋅ P22criticalandb=R⋅T8⋅ Pcritical( 19)criticalcriticalTable 2.1, presents the various thermal properties of some gases and the values of the constants (a,and b) in Van der Waals equation.Download free ebooks at bookboon.com142. Thermodynamics working fluidsEngineering ThermodynamicsSubstanceChemicalFormulaAirO2 +3.76 N2NH3AmmoniaMolarMassM(kg/kmol)28.97GasconstantR (J/kgK)CriticalPressurePC (MPa)286.997CriticalTempTC(K)132.41Van der WaalsConstantsab3.774161.4270.0012617.03488.215405.4011.2771465.4790.00219CarbonDioxideCarbonMonoxideHeliumCO244.01188.918304.207.386188.6430.00097CO28.01296.833132.913.496187.8250.00141He4.0032077.0175.190.229214.0740.00588HydrogenH22.0164124.15733.241.2976112.7440.01321MethaneCH416.042518.283190.704.640888.1810.00266Please click the advertdongenergy.com/jobEverybodyis talking......about future energy supply.
We are not.Stop talking and make a careermoving energy forward.Ambitious engineers andfinance students go todongenergy.com/jobDownload free ebooks at bookboon.com152. Thermodynamics working fluidsEngineering ThermodynamicsNitrogenN228.016296.769126.203.398174.1480.00138OxygenO232.00259.822154.785.080134.3080.00099R12CC12F2120.9268.7593854.12071.7570.00080SulpherDioxideWaterVapourSO264.06129.7894317.870167.7420.00089H2O18.016461.393647.322.0901704.2500.00169Table 2.1 Van Der Waals Constants for some gases2.5 Compressibility of GasesCompressibility factor, Z, is a measure of deviation from the ideal gas.Z=P.vR.T(20)Where v is the specific volume ( V/m ),Note: Z = 1 for an ideal gas.As Z approaches 1 for a gas at given conditions, the behavior of the gas approaches ideal gas behavior.Although, different gases have very different specific properties at various conditions; all gases behavein a similar manner relative to their critical pressure, Pcr and critical temparature, Tcr.Hence, the gas pressures and temperatures are normalized by the critical values to obtain thereduced pressure, PR and temparature, TR.defined asPR=P/Pcr ;TR=T/TcrThe reduced values can then be used to determine Z using the Generalized Compressibility Charts(Figure 2.2)These charts show the conditions for which Z = 1 and the gas behaves as an ideal gas:Download free ebooks at bookboon.com162.
Thermodynamics working fluidsEngineering ThermodynamicsFigure 2.2: Compressibilty Chart2.6 The State Diagram – for SteamProcesses1-2, 2-3, and 3-4 represents a typical constant pressure heating of water which initiallyheated to its boiling point,(1-2),upon continued heat input it starts to evaporate at point 2, itiscompletelyliquid,then gradually someofthe water becomes vapour tillit reaches point3,where allthe water has evaporated, further heating will makethe water vapour superheated(process 3-4).Download free ebooks at bookboon.com172.
Thermodynamics working fluidsEngineering ThermodynamicsDCABicewaterVapourWater-vapourequilibriumFigure 2.3: Formation of Vapour (Steam)Download free ebooks at bookboon.com182. Thermodynamics working fluidsEngineering Thermodynamics2.7 Property Tables And Charts For VapoursTables are normally available which give data for saturated liquid and saturated vapour, a listingfor a given saturation pressure or temperature, some or all of the quantities vf, vg, uf, uf, ug, hf, hfg,hg, sf, sfg and sg. The tables enable u, h or s to be obtained for saturated liquid, wet vapour and drysaturated vapour. Charts for steam are readily available which show h or T as ordinate against s(specific entropy) as abscissa.Please click the advertdongenergy.com/jobdDear highly educated engineeringand finance students,if you are driven, ambitious, open-mindedand focused - we have a challenge for you.Actually, the greatest challenge in theworld.
Curious? Visit dongenergy.com/jobBest wishesDONG EnergyDownload free ebooks at bookboon.com192. Thermodynamics working fluidsEngineering ThermodynamicsFigure 2.4: Temperature – Entropy chart for Water/SteamCourtesy of: http://en.wikipedia.org/Calculations of steam properties in the mixed region:The dryness fraction is an added property needed to define the mixture of water liquid and vapourduring iits transformation ( condensation or evaporation) and is defined as follows:-x=mass of vapourtotal mass of the system(21)The total mass = mass of vapour + mass of liquid; Hence the system volume along the two-phase,process 2-3 (Figure 2.3) is:Download free ebooks at bookboon.com202.
Thermodynamics working fluidsEngineering Thermodynamicsv = (1 − x ) v f + x v g(22)At point state point 2, x = 0at state point 3, x = 1 (Figure 2.3)Values of vf and vg and other properties for real substances are normally given in tables. Suffix ‘f’refers to the liquid; Suffix ‘g’ refers to the dry vapour; and Suffix ‘fg’ refers to the mixed phase.vfg = vg – vfhfg = hg – hfSfg = Sg – SfFor wet steam of dryness fraction xv = (1 – x) . vf + x . vg= vf + x. (vg –vf )= vf + x . vfgSimilar relations for u, h and s.orv = vf + x vfgu = uf + x ufgh = hf + x hfgs = sf + x sfg(23)u = (1 – x) uf + x ugh = (1 –x) hf + x hgs = (1 – x) sf + x sg(24)ptsvfvghfhg(kJ/kg)sf(kJ/kg.K)(kPa)(oC)(m3/kg)(m3/kg)(kJ/kg)1045.810.00114.67410099.630.00104200120.23500151.86sg(kJ/kg.K)191.832,5850.64938.15021.694417.462,6761.30267.35940.001060.8857504.72,7071.53017.12710.001090.3749640.232,7491.86076.8213Download free ebooks at bookboon.com212.
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