my thermodynamics cheat sheets

1 My thermodynamics cheat sheetsNasser M. AbbasiSumemr 2004 Compiled on May 23, 2020 at 4:09am1. all of theormodynamics in one sheet.(a) PDF(b) image2. polytropic process diagrams(a) PDF(b) image3. first and second laws diagrams(a) PDF(b) image4. Gas laws(a) PDF(b) imageAll of theormodynamics in one sheet12 Ideal gas, Any processAny gas, any processGeneral polytropic processIdeal Gas Process classificationreversibleirreversibleP1V1 T1P2V2T2 PVnconstantnconstantVn0constantPn1consta ntTBoundary WorkBoundary WorkBoundary WorkW0 Boundary WorkBoundary WorkP2P1T2T1nn1V1V2nwRT1lnP1P2RT1ln21P11 ln21u2u1 CvT2T1h2h1 CpT2T1s2s112 QTsgenmass c onstants2s112C0 TdTRln21s2s112Cp0 TdTRlnP2P1 Assume constant specific heats2s1C0lnT2T1 Rln21s2s1Cp0lnT2T1 RlnP2P1 Table s1 sT20 sT10 RlnP2P1 Using Table or work (for FLOW process only)

2 Wn1nPeePiinR1nTeTiwP22P221nRT2T11nwP22P2 21kRT2T11kwP22P22RT2T1 Shaft work (for FLOW process only)W0 Shaft work (for FLOW process only)wPiilnPePiRTilnPePiRTilneiShaft work (for FLOW process only)wk1kPeePiikR1kTeTiShaft work (for FLOW process only)n1n1wPeePiiRTeTiVerify this, what volume is this?dsQTWPdV1stLawQWUTdsdUPdVSubstitute into Substitute into TdSdHVdP 1 2 3 4 5 Gibbs equationsenthlapylawHUPVsodHdUPdVVdpSpec ialized polytropic processes work formulasGeneral formulas for reversible compressible processes formulas for general polytropic process Introduc tion to thermodynamics , equations .

3 By Nasser M 2004 SolvingEntropy change determination formulas, for an ideal gas, ANY process typeEntropy change determination formulas, for an ideal gas, polytropic process typeGeneral polytropic relations2s1Cv0R1nlnT2T1s2s1Cv0lnT2T1s2s 1Cp0lnT2T1s2s10 Entropy changeEntropy changeEntropy changeEntropy changen=k, constant entropywiePw12 PShaft WorkTotal specific work for steady state flow process where only shaft work is involved (no boundary work). Valid for ANY reversible process (do not have to be polytropic)wtotal ievdP Vi2 Ve22 g Zi Ze wiePwiePwiePdu Cv0dTdh Cp0dTCp0 Cv0 Rs2 s1 RlnP2P1 GASds CpdTT RdPPSolids/LiquidsdP 0(incompressible),andd 0dh dudh CdTIdeal Gash u P dh du d P dh du Pd vdPP RTsoh u RTdh du RdTdh CvdT RdTdh h1 ClnT2T1h2 h1 CplnT2T1 Entropy change equationSolids/LiquidsIdeal Gasds dqT(bydefinition,entropylaw) dw duT dwT duT 1Td Pv 1Td CvT 1T Pdv vdP CvTdT PTdv vTdP CvdTTbutPv RT,henceds Rdvv RdPP CvdTTs2 s1 Rlnv2v1 RlnP2P1 CvlnT2T1 1 How to get this below from the above?

4 ?ds dqT(bydefinition,entropylaw) dw duT dwT duT 1Td Pv 1 TdCT 1 TPdv vdP CvTdT PTdv vTdP CvdTTbutdP 0sinceincompressible,anddvisverysmall,so ds CdTTs2 s1 ClnT2T1 1 Q W dEwhereE U KE PEEnthlapy definitionFirst lawFlowNon-FlowQ1,2 W1,2 m u2 u1 Or, it c an be written as follows (ignoring KE and PE changes to the control mass)As a Rate equationQ W dEdtNon-steady state (Transient, state change)Q m i h KE PE i W m e h KE PE e m h KE PE i m h KE PE mhi m he hi Steady state devices: heat exchanges, Nozzle, Diffuser, Throttle, Turbine, Compressors and mi h KE PE i me h KE PE e m2u2 m1u1 General equation.

5 Valid at any instance of time. Steady or not steady Simplifies mihi mehe m2u2 m1u1 me mq w he hi hehihim1m2 State 1 State 2 Sec ond lawNon-flowm s2 s1 QT Sgens2 s1 qT sgenflowsteadytransient0 misi mese QT Sgen0 si se qT sgenm2s2 m1s1 misi mese qT sgenFigure 1: thermodynamics3P1 V1 T1 State 1P2 V2 T2 State 2 PVnconstantPolytropic processWe have a total of 7 unknowns. 3 in state 1, 3 in state 2, and n, the polytrpoic process given any 5 out of these 7, then the remaining 2 can be example, if we know T1, P1, V1, n, P2, then we can find V2, and T2 Polytrpoic processby Nasser M 2004n=0 const PnconstantVPvn=1, const Tn=k, adiapatic, const SEXPANSION QUADRANTCOMPRESSIONQUADRANTI gnore this quadrant in real engineering equipmentsIgnore this quadrant in real engineering equipmentsInitial state pointn=1 const TTsn=0, const PEXPANSION QUADRANTCOMPRESSIONQUADRANTI nitial state pointn=k const SClock wise, n=0,1,k.

6 InfinityClock wise, n=0,1,k,infinitynconstantVIgnore this quadrant in real engineering equipmentsIgnore this quadrant in real engineering equipmentsHeat OUT processesHeat IN processesHeat IN processesHeat OUT processesProcess lines to left of adiabatic line means negative Q ( heat OUT), on the right are positive Q ( heat IN) processFigure 2: polytropic process diagrams4 Laws of thermodynamicsFirst lawSecond lawThis is also called the law of conservation of energyChapter 5. 1st Law for control massQ1 2 W1 2 E2 E1E U PE KEChapter enthalpyH U PVh u PvDerived from first Law by setting P constant Q W m u2 u1 Q PdV m u2 u1 Q P V2 V1 m u2 u1 q P 2 1 u2 u1 q P 2 u2 P 1 u1 1q2 h2 h1 Note: Even though enthlapy was derived by the assumption of constant P, it is a property of a system state regardless of the process that lead to the CvCpSpecific heat is the amount of heat required to raise the temp.

7 Of a unit mass by one degreeCv u TvCp h TpSolids and liquids: Use average specific heat C. dh du d Pv dh du vdP Pdv Forsolidsandliquids,dv 0dh du vdP ForSolidsandLiquidsAlsoforsolidsandliqui ds,visverysmall,hencedh duForSolidsandLiquidssincealmostincompre ssible,henceCv CvForsolidsandliquidsFor solids and liquidsHenceforsolids/liquids,dh du CdTFor ideal gasdu Cv0dTdh Cp0dTCp0 Cv0 RChapter 61st Law for control volumeQin Win mi h PE KE i Qout Wout me h PE KE e m2u2 m1u1 Steady stateTransient StateAdiabatic processWnet he hiWnethehiThe entropy of an isolated system increases in all real processes and is conserved in reversible AVAILABLE energy of an isolated system decreases in all real processes (and is conserved in reversible processes)The 2nd law says that work and heat energy are not the same.

8 It is easier to convert all of work to heat energy, but not vis versa. work energy is more valuable than heat energy. heat can not be converted completely and continuously into , 2nd law dictates the direction at which a system state will change. It will move to a state of lesser available energyEntropy is constant in a reversible adiabatic S1 12 QT SgenSgen 0 Sgen 0 reversibleprocess Q 0 adiabaticprocessHence,S2 S1forareversibleadiabaticprocessWlost TdSgenActualboundaryworkW1 2 PdV WlostGibbsrelationsTds du PdvTds dh vdpSolids, Liquidss2 s1 ClnT2T1 Ideal GassT0 T0 TCp0 TdTs2 s1 sT20 sT10 s1 Cp0lnT2T1 RlnP2P1 ConstantCp,Cvs2 s1 CvlnT2T1 Rlnv2v1 ConstantCp,Cvk Cp0Cv0 PolytrpicprocessPVn constantP2P1 V1V2nP2P1 T2T1nn 1specificwork(workismovingboundarywork.)

9 Pdvw1 2 11 n P2v2 P1v1 R1 n T2 T1 n 1w1 2 P1v1lnv2v1 RT1lnv2v1 RT1lnP1P2n 1By Nasser M. 3: first and second laws diagrams5 Solids/liquidsIdeal gas, Any processAny gas, any processGeneral polytropic processIdeal Gas Process classificationreversibleirreversibleP1V1 T1P2V2T2 PVnconstantnconstantVn0constantPn1consta ntTBoundary WorkBoundary WorkBoundary WorkW0 Boundary WorkBoundary WorkP2P1T2T1nn1V1V2nwRT1lnP1P2RT1ln21P11 ln21u2u1 CvT2T1h2h1 CpT2T1s2s112 QTsgenmass c onstants2s112C0 TdTRln21s2s112Cp0 TdTRlnP2P1 Assume constant specific heats2s1C0lnT2T1 Rln21s2s1Cp0lnT2T1 RlnP2P1 Table s1 sT20 sT10 RlnP2P1 Using Table or work (for FLOW process only)

10 Wn1nPeePiinR1nTeTiwP22P221nRT2T11nwP22P2 21kRT2T11kwP22P22RT2T1 Shaft work (for FLOW process only)W0 Shaft work (for FLOW process only)wPiilnPePiRTilnPePiRTilneiShaft work (for FLOW process only)wk1kPeePiikR1kTeTiShaft work (for FLOW process only)n1n1wPeePiiRTeTiVerify this, what volume is this?dsQTWPdV1stLawQWUTdsdUPdVSubstitute into Substitute into TdSdHVdP 1 2 3 4 5 Gibbs equationsenthlapylawHUPVsodHdUPdVVdpSpec ialized polytropic processes work formulasGeneral formulas for reversible compressible processes formulas for general polytropic process Introduc tion to thermodynamics , equations .