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13gas_relation

# 13gas_relation - Some Relationships for Gases these are...

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Some Relationships for Gases define some units these are extracted from Van Wylen & Sonntag, Fudamentals of Classical 3 kJ := 10 J Thermodynamics, Third Edition to which page numbers and equation numbers apply 2006: included reference to text: Woud section 2.23 in [W n.nn] 3 kmol := 10 mole section 3.4 Equations of state for the vapor phase of a simple compressile substance - page 41 (Woud page 20) gas at low density (experiment) pv = R R = universal_gas_constant (3.1) T xxx = mole_basis kJ kJ R_bar := 8.3144 units sometimes . .. kmol K kg_mol K R R = mw mw = molecular_weight for R_bar above mw = kg kmol p 1 v 1 p 2 v 2 [W 2.32, 2.33[ (3.5) pV = mR T or . .. pv = RT (3.2) = T 1 T 2 section 4.3 Work done at moveable boundary of simple compressible system - page 63 W 1_2 p 1 V 1 p 1 V 1 (4.5) if . .. n = constant n = 1 = V 2 p dV = V 2 1 dV = ln V 2 V 1 V 1 V V 1 section 5.6 The Constant-Volume and Constant-Pressure Specific Heats - page 98 specific heat = increment of heat Q to change T by 1 deg c = 1 δ Q 1 = specfic m δ T m two cases: 1) constant volume c v = 1 δ Q constant volume m δ T = δ W (5.4) 1st law . .. δ Qd E + δ W = dU + dKE + dPE + δ U + p ⋅δ V dKE = dPE = 0 δ W = p V = = 0 1 δ Q 1 δ U δ u c v δ u δ T = constant volume (5.14) [W 2.36] c v = = = m δ T m δ T δ T 2) constant pressure δ + p V = δ H as . ... dH = d U + ) = dU + p dV + = ( p V Vdp dp = 0 1 δ Q 1 δ H δ h c p δ h δ T = constant pressure (5.15) [W 2.37] c p = = = m δ T m δ T δ T 10/23/2006 1

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section 5.7 The Internal Energy, Enthalpy and Specific Heats of Ideal Gases - page 100 u () experiment (Joule) ideal gas pv = RT = f T => constant volume δ u c v = u not a function of v => du = c vo dT vo ideal gas (5.20) δ T also . .. p v () RT = hT h = u + = uT + () i.e. h = F(T) only (5.24) δ h dh = c po dT po => constant pressure δ T c p = => ideal gas dh du relation between c vo and c po ... h = u + p v = u + R T = + R differentiate w.r.t T dT dT c po = c vo + R or . .. c po c vo = R (5.27) with constant c h 2 h 1 = c po ( T 2 T 1 ) otherwise integrate if c(T) known or tables (5.29) [W 2.38] section 7.10 Entropy Change of an Ideal Gas - page 206 Tds = du (7.7) [W 2.18] + p dv T => T du = c vo dT and . .. = => p = R = c vo dT + R dv v v T 2 v 2 c vo = constant dT dv ds = + R (7.19) c vo T 1 Rln v 1 s 2 s 1 = ln + (7.24) c vo T v otherwise integrate or use tables v dp = dh (7.7) [W 2.21] T T dh = c po
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13gas_relation - Some Relationships for Gases these are...

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