MEEN 315 Formula Sheet for Exams First Law of Thermodynamics DE Q W energy balance for closed system dE Q W energy rate balance for closed system dt dEcv V2 V2 Qcv Wcv mi hi i gzi me he e gze energy rate balance for control volume dt 2 2 i e 2 2 V V 0 Qcv Wcv mi hi i gzi me he e gze energy rate balance for control volume at steady state 2 2 i e 2 2 V V2 1 inlet 1 exit control volume at steady state 0 Qcv Wcv m h1 h2 1 g z1 z2 2 Second Law of Thermodynamics 2 dQ S2 S1 s 1 T b Qj dS s dt j Tj closed system entropy balance closed system entropy rate balance Qj dScv mi si me se s cv dt j Tj i e 0 j Qj Tj mi si me se s cv i control volume entropy rate balance control volume entropy rate balance at steady state e Conservation of Mass dmcv mi me dt i e m m i i e Steady State e Properties E KE PE U 1 mV 2 mgz mu 2 h u pv Thermodynamic Cylce h g Wcycle Qin Wcycle b Power cycle Qin Qout Q out Wcycle Wcycle Qin Q in Wcycle Wcycle Refrigeration cycle Heat pump cycle Quality Equation x mvapor mliquid mvapor mvapor m v 1 x v f xvg v f x vg v f u 1 x u f xu g u f x u g u f h 1 x h f xhg h f x hg h f s 1 x s f xsg s f x sg s f 1 MEEN 315 Formula Sheet for Exams Isentropic Efficiencies ht Wt m W actual Turbine Wt m s Wideal hp Wp m s Wp m Wideal Pump or compressor Wactual Flow Relationships m AV v Boundary Work V2 W p dV V1 W p V2 V1 p V p1V1 W 2 2 1 n V W pV ln 2 V1 Constant Pressure Polytropic Process pVn constant Polytropic Process n 1 Ideal Gas Relationships pv RT du cv T dT dh c p T dT pV mRT pV nRT Du cv DT at constant Cv Dh c p DT at constant Cp T2 s T2 v2 s T1 v1 cv T T1 s T2 p2 s T1 p1 s o T2 s o T1 R ln Z pv RT pR p pc T2 v dT R ln 2 T v1 TR T Tc s T2 p2 s T1 p1 c p T T1 p2 p1 vR v RTc pc Ideal Gas Isentropic Relationships p2 pr 2 p1 pr1 T2 v1 T1 v2 v2 vr 2 v1 vr1 k 1 T2 p2 T1 p1 k 1 k p2 v1 p1 v2 Solid Liquid Relationships Dh Du cDT Tds Relations Tds du pdv T Ds c ln 2 T1 Tds dh vdp 2 k p dT R ln 2 T p1
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