Thermodynamics Cheat Sheet, Cheat Sheet of Thermodynamics

Download Thermodynamics Cheat Sheet and more Cheat Sheet Thermodynamics in PDF only on Docsity! my thermodynamics cheat sheets Nasser M. Abbasi Sumemr 2004 Compiled on May 23, 2020 at 4:09am 1. all of theormodynamics in one sheet. (a) PDF (b) image 2. polytropic process diagrams (a) PDF (b) image 3. first and second laws diagrams (a) PDF (b) image 4. Gas laws (a) PDF (b) image All of theormodynamics in one sheet 1 2 Ideal gas, Any process Any gas, any process General polytropic process Ideal Gas Process classification reversibleirreversible P1 V1 T1 P2 V2 T2 P V n constant n constant V n 0 constant P n 1 constant T Boundary Work Boundary Work Boundary Work W 0 Boundary Work Boundary Work P2 P1 T2 T1 n n 1 V1 V2 n w R T1 ln P1 P2 R T1 ln 2 1 P1 1 ln 2 1 u2 u1 Cv T2 T1 h2 h1 Cp T2 T1 s2 s1 1 2 Q T sgen mass constant s2 s1 1 2 C 0 T dT R ln 2 1 s2 s1 1 2 Cp0 T dT R ln P2 P1 Assume constant specific heat s2 s1 C 0 ln T2 T1 R ln 2 1 s2 s1 Cp0 ln T2 T1 R ln P2 P1 Table A.6 s2  s1  sT2 0  sT1 0   R ln P2 P1 Using Table A.7 or A.8 WORK Shaft work (for FLOW process only) w n 1 n Pe e Pi i n R 1 n Te Ti w P2 2 P2 2 1 n R T2 T1 1 n w P2 2 P2 2 1 k R T2 T1 1 k w P2 2 P2 2 R T2 T1 Shaft work (for FLOW process only) W 0 Shaft work (for FLOW process only) w Pi i ln Pe Pi R Ti ln Pe Pi R Ti ln e i Shaft work (for FLOW process only) w k 1 k Pe e Pi i k R 1 k Te Ti Shaft work (for FLOW process only) n 1 n 1 w Pe e Pi i R Te Ti Verify this, what volume is this? ds Q T W P dV 1 st Law Q W U T ds dU P dV Substitute into Substitute into T dS dH V dP 1 2 3 4 5 Gibbs equations enthlapy law H U P V so dH dU P dV V dp Specialized polytropic processes work formulas General formulas for reversible compressible processes formulas for general polytropic process Introduction to Thermodynamics, equations. By Nasser M Abbasi image2.vsd August 2004 Solving Entropy change determination formulas, for an ideal gas, ANY process type Entropy change determination formulas, for an ideal gas, polytropic process type General polytropic relation s2 s1 Cv0 R 1 n ln T2 T1 s2 s1 Cv0 ln T2 T1 s2 s1 Cp0 ln T2 T1 s2 s1 0 Entropy change Entropy change Entropy change Entropy change n=k, constant entropy w i e P w 1 2 P Shaft Work Total 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   i e v dP  Vi 2Ve2 2  gZi  Ze w i e Pw i e P w i e P du  Cv0 dT dh  Cp0 dT Cp0  Cv0  R s2  s1  R ln P2 P1 GAS ds  Cp dTT  R dP P Solids/Liquids dP  0 (incompressible), and d  0 dh  du dh  C dT Ideal Gas h  u  P dh  du  dP dh  du  P d  v dP P  RT so h  u  RT dh  du  R dT dh  CvdT  RdT dh  CpdT Process that causes irreversibility 1. Friction 2. Unrestrained expansion 3. Heat transfer from hot to cold body 4. Mixing of 2 differrent substances 5. i2R loss in electric circuits 6. Hystereris effects 7. Ordinary combustion h2  h1  C ln T2 T1 h2  h1  Cp ln T2 T1 Entropy change equation Solids/Liquids Ideal Gas ds  dq T (by definition, entropy law)  dw  du T  dw T  du T  1 T dPv  1 T dCvT  1 T P dv  v dP  Cv T dT  P T dv  v T dP  Cv dTT but Pv  RT, hence ds  R dvv  R dP P  Cv dTT s2  s1  R ln v2 v1  R ln P2 P1  Cv ln T2 T1 1 How to get this below from the above?? ds  dq T (by definition, entropy law)  dw  du T  dw T  du T  1 T dPv  1 T d C T  1 T P dv  v dP  Cv T dT  P T dv  v T dP  Cv dT T but dP  0 since incompressible, and dv is very small, so ds  C dT T s2  s1  C ln T2 T1 1 Q  W  dE where E  U  KE  PE Enthlapy definition First law FlowNon-Flow Q1,2  W1,2  mu2  u1  Or, it can be written as follows (ignoring KE and PE changes to the control mass) As a Rate equation Q  W  dE dt Non-steady state (Transient, state change) Q C.V.  m ih  KE  PEi  W C.V.m eh  KE  PEe  dE dt QC.V.  mh  KE  PEi  WC.V.mh  KE  PEe QC.V.  mhi  WC.V.mhe QC.V.  WC.V.mhe  hi  Steady state devices: Heat exchanges, Nozzle, Diffuser, Throttle, Turbine, Compressors and Pumps QC.V.  mih  KE  PEi  WC.V.meh  KE  PEe  m2u2  m1u1  General equation. Valid at any instance of time. Steady or not steady flow. Usually Simplifies to QC.V.  mihi  WC.V.mehe  m2u2  m1u1  steady state. mi  me  m q  w  he  hi heh i h i m1 m2 State 1 State 2 Second law Non-flow ms2  s1   Q T  Sgen s2  s1  q T  sgen flow steady transient 0  misi  mese  Q T  Sgen 0  si  se  q T  sgen m2s2  m1s1  misi  mese  q T  sgen Figure 1: thermodynamics