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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 + " m(h + + gz) # " m(h + + gz) Open system: dt 2 2 in out Second Law: 1 S2 " S1 = # dQ + $ Closed system: Tb ! dS Q = "± + " m s # " 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/dT

v = V/m k = cP / cV

R = cP - cV

x = mvapor / mtotal

W =

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:

" P dV

PV = C PVk = C

m = " AV

dm = "m # "m dt in out

Isentropic efficiencies:

!

T = Wact/Wisen

!

C = Wisen/Wact

k

N = V2/Vs2

T2 " P2 % =$ ' T1 # P1 &

k(1 k

Isentropic process of an ideal gas: Carnot cycles:

P2 " V1 % =$ ' P1 # V2 &

T2 " V1 % =$ ' T1 # V2 &

k(1

QH / QL = TH / TL

= 1 - TL / TH for Carnot power cycle Heat pump = QH / WNET

! ! Coefficient of Performance: Refrigerator ! = QC / WNET

Availability: 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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