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`THERMODYNAMIC EQUATION SHEET First Law: E = m(u + v2/2 + gz) h = u + pv = u + p/ Closed system: E = Q - W dE V2 V2     = ±Q ± W + &quot; m(h + + gz) # &quot; m(h + + gz) Open system: dt 2 2 in out Second Law: 1 S2 &quot; S1 = # dQ + \$ Closed system: Tb !  dS Q    = &quot;± + &quot; m s # &quot; m s + \$ Open system: dt T in out Ideal Gas Law: Specific Heats: Phase change: Boundary Work:!!PV = NRuT m = N*M Ru = 8314 J/kmol-K R = Ru / M cP = dh/dT cV = du/dTv = V/m k = cP / cVR = cP - cVx = mvapor / mtotalW =umix = (1-x)*uf + x*ug (also true for h, v, s)Isothermal process of ideal gas: Isentropic process of ideal gas:! Conservation of mass:&quot; P dVPV = C PVk = C m = &quot; AVdm   = &quot;m # &quot;m dt in outIsentropic efficiencies:!T = Wact/Wisen!C = Wisen/WactkN = V2/Vs2T2 &quot; P2 % =\$ ' T1 # P1 &amp;k(1 kIsentropic process of an ideal gas: Carnot cycles:P2 &quot; V1 % =\$ ' P1 # V2 &amp;T2 &quot; V1 % =\$ ' T1 # V2 &amp;k(1QH / QL = TH / TL = 1 - TL / TH for Carnot power cycle Heat pump  = QH / WNET! ! Coefficient of Performance: Refrigerator !  = QC / WNETAvailability: X = (E - Uo) + P(v-vo) - To(S - So) Flow exergy:  = (h-ho) +To(s-so) + V2/2 + gz Properties of air @ STP: k = 1.4 R = 287 J/kg-K a = 330 m/s  = 1.2 kg/m3 cP = 1005 J/kg-K cV = 718 J/kg-K M = 29 kg/kmol`

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