Lecture. Polymer Thermodynamics 0331 L Chemical Potential
|
|
- Garey York
- 5 years ago
- Views:
Transcription
1 Prof. Dr. rer. nat. habl. S. Enders Faculty III for Process Scence Insttute of Chemcal Engneerng Department of Thermodynamcs Lecture Polymer Thermodynamcs 033 L Chemcal Potental
2 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture state quanttes can be extensve or ntensve. 2 Extensve state quanttes wll double hs value f two equal systems wll be unted to one new system..e. mass m, volume V, energy U Intensve state quanttes wll eep hs value f two equal systems wll be unted to one new system..e. temperature T, pressure P, molar volume v, specfc volume v sp molar quanttes v = V n n = amount of substance densty [g/l] concentraton [mol/l] specfc quanttes v sp V = = m m = mass, M = molar mass v M
3 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 3 Mxtures are characterzed by composton. mole fracton: mole fracton of a component,, n a mxture s the relatve proporton of molecules belongng to the component to those n the mxture, by number of molecules. x n = x = n = weght (mass) fracton: weght fracton of a component,, n a mxture s the relatve proporton of weght belongng to the component to those n the mxture, by weght of molecules. relaton: n = w m M m = w = m =
4 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 4 Volume fracton: volume fracton of component,, of a mxture s defned as the quotent of the volume of the component,, and the whole volume. φ V = φ = V = ttenton: volume fractons depends on temperature and pressure. V m g n mol = ρ = V = ρ = ρ sp m m ρ m m relatons: 3 3 sp
5 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 5 We consder a mxture consstng of three gases (, and C). t equal values for pressure and temperature all three gases have accordng to the deal gas law the volumes V, V and V C. fter the mxng the whole volume has the value V. T,P = constant V V V C PV = nrt Removng the walls V V = V + V + V property of deal mxture C
6 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 6 V = V + V + V C propertes of deal mxture For deal mxtures at constant pressure and at constant temperature t s essental that the sum of the volumes of sngle gases, V, results n the volume of the mxture,v. deal mxture of gases mxture of deal gases Defnton of deal Gas: no ntermolecular forces and partcles have zero volume Defnton deal mxture: no statement about the ntermolecular forces between molecules of equal type and no statement about the partcle volume; the deal mxture can formed from deal or real gases Ideal gases buld up always an deal mxture. Real gases can form an deal mxture, dependng from ther nature.
7 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 7 Ideal gas: I =0 I = nteracton Ideal mxtures of gases: I =I =I Ideal gases buld up always an deal mxture. Real gases can form an deal mxture, dependng from ther nature.
8 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 8 V m V = V + V + V C extensve 3 v = V n 3 v m mol alternatve v sp, = V m v sp 3 m g nv = v n + v n + v n C C v n v n v n v = + + C n n n v = v x + v x + v x ntensve C C C
9 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 9 In a mxture of gases, each gas,, has a partal pressure, P, whch s the pressure whch the gas would have f t alone occuped the volume at constant temperature. defnton: P = xp P = P + P + P + = P C = Ths equaton holds true for deal and real mxtures of gases. Furthermore, n the case of deal mxtures of gases the followng equaton s vald: P = nrt V Dalton s Law
10 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 0 thought experment: sothermal expanson P = = P C mxng of, and C P = P + P + P C
11 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture ll thermodynamc quanttes of the frst law of thermodynamcs n an deal mxture are addtve. example: H h = n H = nh H = H + H + H + = H / n C = H H H HC H = = n n n n n h = nh nh nh nh n n n n C C = = = h= x h + x h + x h + = xh C C =
12 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 2 ll thermodynamc quanttes of the second law of thermodynamcs n an deal mxture are not addtve. Reason: For all mxtures (also deal mxtures) result an entropy of mxng. T,P = constant + V V 2 V=V +V 2 Δ S =Δ S +Δ S = S S + S S end start end start Mx deal gases: T,P = constant C P P nr T T T V v ds = dt + dv = dv = dv
13 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 3 Δ S =Δ S +Δ S = S S + S S end start end start Mx deal gas: T,P = constant S nr ds = dv ds = nr dv V start start V S end end end start V V + Vj S S = nr ln nr ln start = V V V + V V + V Δ MxS = nrln + nrln V V V = x V V = x V V V end
14 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 4 deal gas: T,P = constant V + V V + V Δ MxS = nrln + nrln V V V = x V V = x V x + x = x V + x V x V + x Δ MxS = nrln + nr V ln x V x V Δ S = n Rln x n Rln x = nr x ln x + x ln x ( ) ( ) ( ) ( ) ( ) Mx Δ S = nr x ln x entropy of mxng for deal mxture ( ) Mx =
15 Polymer Thermodynamcs 3. Chemcal Potental 3.. Ideal mxture 5 Δ S = nr x ln x ( ) Mx = Entropy of mxng for deal mxture G = H TS Δ G =Δ H TΔ S Mx Mx Mx Δ H = 0 for deal mxtures Δ G = T Δ S Mx Mx Mx Δ G = nrt x ln x ( ) Mx = F = U TS Δ F =Δ U TΔ S Gbbs energy of mxng for deal mxture Mx Mx Mx Δ U = 0 for deal mture Δ F = T Δ S Mx Mx Mx Δ F = nrt x ln x Helmholtz energy for deal mxture ( ) Mx =
16 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 6 Types of mxtures Homogenous mxtures havng deal or real behavor Heterogeneous mxtures conssts of two or more phases Interm znc sulfde surfactant
17 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture v 0 =58.7 ml/mol 7 60 water () + ethanol () v [ml/mol] deal real real mxture T=25 C v 0 =8. ml/mol 0,0 0,2 0,4 0,6 0,8,0 X Ethanol deal real deal E v = v0x + v0x v = v + v v E excess volume = mxng volume
18 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture v [ml/mol] deal real 0,0 0,2 0,4 0,6 0,8,0 X Ethanol v E [ml/mol] 0,0-0,5 -,0 -,5-2,0 0,0-0,5 -,0 -,5-2,0-2,5-2,5 0,0 0,2 0,4 0,6 0,8,0 X Ethanol mxng volume v E volume of mxture v real
19 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 9 v0 deal real deal E v = v0x + v0x v = v + v molar volume of component = pure-component volume real v = x v + x v v partal molar volume of component pure-component volume Partal molar volumes depend on the composton of real mxture.
20 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 20 Ideal gas: I =0 Ideal mxture I =I =I Real mxture I I I
21 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 2 v real v = x v + x v partal molar volume of component pure-component volume V = f( T, P, n, n ) 2 V V V V dv = dt + dp + dn + dn T P n n 2 Pn,, n Tn,, n PT,, n 2 PT,, n V V = v = n n PT,, n 2 PT,, nj ì v Defnton of partal molar quanttes
22 V = Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture f( T, P, n, n ) 2 V V V V dv = dt + dp + dn + dn T P n n 2 Pn,, n Tn,, n PT,, n 2 PT,, n V V = v = v n n PT,, n 2 PT,, nj ì Defnton of partal molar quanttes 22 dt = dp = 0 V V dv = dn + dn = v dn + v dn n dv = PT,, n n2 PT,, n = 2 vdn
23 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 23 dt = dp = 0 dv = v dn V = n v ( ) dv = n dv + v dn = v dn = = = = = ndv = 0 Gbbs - Duhem equaton t sothermal sobarc condtons partal molar volumes depend on each other.
24 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture = = = = dt dp n dv bnary mxture made from and ndv + ndv = 0 ndv = ndv xdv = xdv = ( x) dv x dv dv = ( x ) dx dx TP, TP, x dv dv + ( x ) = 0 dx dx TP, TP,
25 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 25 v v real =v deal +v E v deal =x v 0 +x v v [ml/mol] v E v real =x v +x v 6 6 0,0 0,2 0,4 0,6 0,8,0 8 v x
26 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture v 0 v v 0 25 v [ml/mol] 20 5 v ,0 0,2 0,4 0,6 0,8,0 x For pure components vald: v =v 0
27 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 27 dv dv dt = dp = 0 v = x v x + ( x ) = 0 v= x v + x v = x v + x v = dx dx TP, TP, ( ) v v v = x + v + ( x ) v = v v x x x TP, TP, TP, v x TP, = v v
28 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture Data nalyss example v E = x x 28 expermental data v [ml/mol] v E v deal 20 0,0 0,2 0,4 0,6 0,8,0 x v E [ml/mol],0 0,5 0,0-0,5 -,0 -,5-2,0-2,5 v E =f(x )=x x * -3,0 0,0 0,2 0,4 0,6 0,8,0 x
29 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 29 real deal E v = v + v = xv0 + xv0 + xx = xv + x v x v = real TP, xv + xv + xx x x 0 0 ( 2 ) = v v + x 0 0 v v v = + + v x x x real x v x TP, TP, TP, real v v v = x + x + v v = v v x x TP, x TP, TP, 0 v Gbbs-Duhem equaton v
30 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture 30 real real v v v0 v0 ( 2x) x x TP, TP, ( 2 ) v v v ( 2 ) = + = v v v v + x = = v v + x + v v ( 2 ) = v v + x + v 0 0 v = v + x v = v + x = xv + xv xv + xx,0 x 0 0 v E [ml/mol] 0,5 0,0-0,5 -,0 -,5-2,0-2,5-3,0 0,0 0,2 0,4 0,6 0,8,0 x v E =f(x )=x x *
31 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture data analyss alternatve possblty startng pont (defnton): V n PT,, nj ì = v 3 nv v n v v = = n + v = n + v n n P, T, n n P, T, n n P, T, n P, T, n nv v n v v = = n + v = n + v n n P, T, n n P, T, n n P, T, n P, T, n = =
32 Polymer Thermodynamcs 3. Chemcal Potental 3.2. Volume of real mxture data analyss alternatve possblty 32 v v v = n + v and v = n + v n PT,, n n PT,, n PT,, n real deal E our example v = v + v = xv0 + xv0 + xx real n n nn v = v0 + v0 + 2 n n n v n n n n n = v v n n n n ( ) ( ) n n n n n v = n v 2 0 v n n n v = v + x 2 0 n n n n v + v + n n n 0 0 2
33 Polymer Thermodynamcs 3. Chemcal Potental 3.3. Generalzaton 33 Generalzaton for any state functon Z Z = f( T, P, n, n ) 2 Z Z Z Z dz = dt + dp + dn + dn T P n n 2 Pn,, n Tn,, n PT,, n 2 PT,, n Z n PT,, nj ì = z The partal molar quantty of component,, s the partal dervaton of an extensve state functon accordng the amount of mole at constant pressure, constant temperature and constant amount of mole of all other components.
34 Polymer Thermodynamcs 3. Chemcal Potental 3.3. Generalzaton 34 Generalzaton to any state functon Z H = f( T, P, n, n ) 2 H H H H dh = dt + dp + dn + dn T P n n 2 Pn,, n Tn,, n PT,, n 2 PT,, n H n PT,, nj ì = h The partal molar quantty of component,, s the partal dervaton of an extensve state functon accordng the amount of mole at constant pressure, constant temperature and constant amount of mole of all other components.
35 Polymer Thermodynamcs 3. Chemcal Potental 3.3. Generalzaton 35 ll thermodynamc mxng quanttes of the frst law of thermodynamcs are not zero for real mxtures..e. mxng enthalpy Δ Mx H calorc effects that occur durng the producton of real mxtures.e. dluton of sulfurc acd usng water leads to temperature change Δ H = H H Mx end start H = n h + n h H = n h + n h start 0 0 end ( ) + ( ) Δ H = nh + nh nh nh = n h h n h h Mx Δ H = n h + n h = H E E E Mx Vdeo H E can be measured.e. H 2 SO 4 95 J/mol
36 Polymer Thermodynamcs 3. Chemcal Potental 3.3. Generalzaton 36 G = f( T, P, n, n ) 2 bnary mxture G G G G dg = dt + dp + dn + dn T P n n 2 Pn,, n Tn,, n PT,, n 2 PT,, n Z n PT,, nj ì = z G n PT,, nj ì = μ The chemcal potental of component, μ, s the partal dervaton of the extensve state functon free enthalpy accordng the amount of mole of the consdered component at constant pressure, temperature und amount of mole of all other components n the mxture. Hence the chemcal potental s the partal molar quantty of the free enthalpy.
37 Polymer Thermodynamcs 3. Chemcal Potental 3.3. Generalzaton 37 G = f( T, P, n, n ) 2 bnary mxture G G G G dg = dt + dp + dn + dn T P n n 2 Pn,, n Tn,, n PT,, n 2 PT,, n G G = S = V T P Pn,, n Tn,, n 2 2 dg = SdT + VdP + μ dn + μ dn 2 2 Generalzaton of mxtures contanng -components dg = SdT + VdP + μdn = Gbbs fundamental equaton Ths equaton contans all thermodynamc nformaton of mxtures.
38 Polymer Thermodynamcs 3. Chemcal Potental 3.3. Generalzaton 38 F = f( T, V, n, n ) 2 bnary mxture F F F F df = dt + dv + dn + dn T V n n 2 Vn,, n Tn,, n TVn,, 2 TVn,, F F = S = P T V Vn,, n Tn,, n 2 2 df = SdT PdV + μ dn + μ dn 2 2 Generalzaton of mxtures contanng -components. df = SdT PdV + μdn = Gbbs fundamental equaton Ths equaton contans all thermodynamc nformaton of mxtures.
39 Polymer Thermodynamcs 3. Chemcal Potental 3.3. Generalzaton 39 U = f( V, S, n, n ) 2 bnary mxture U U U U du = dv + ds + dn + dn V S n n 2 Sn,, n Vn,, n V, S, n 2 V, S, n U U = P = T V S Sn,, n Vn,, n 2 2 du = PdV + TdS + μ dn + μ dn 2 2 Generalzaton of mxtures contanng -components. du = TdS PdV + μdn = Gbbs fundamental equaton Ths equaton contans all thermodynamc nformaton of mxtures.
40 Polymer Thermodynamcs 3. Chemcal Potental 3.3. Generalzaton 40 H = f( P, S, n, n ) 2 bnary mxture H H H H dh = dp + ds + dn + dn P S n n 2 Sn,, n Pn,, n PSn,, 2 PSn,, H H = V = T P S Sn,, n Pn,, n 2 2 dh = VdP + TdS + μ dn + μ dn 2 2 Generalzaton of mxtures contanng -components. dh = TdS + VdP + μdn = Gbbs fundamental equaton Ths equaton contans all thermodynamc nformaton of mxtures.
41 dg = SdT + VdP + μdn Polymer Thermodynamcs 3. Chemcal Potental = 3.3. Generalzaton () ()+(2) Vn, Pn, 4 F G = = S T T df = SdT PdV + μdn = (2) (2)+(3) U F = = P V V Sn, Tn, = + μ (3) (3)+(4) S = Vn, S Pn, du TdS PdV dn U H = = T dh = TdS + VdP + μdn = (4) ()+(4) H G = = P P Sn, Tn, V U H F G = = = = n n n n SVn,, SPn,, TVn,, TPn,, j j j j μ
42 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum a) thermc equlbrum: T I = T II =... = T constant temperature b) mechancal equlbrum: P I = P II =... = P constant pressure c) materal equlbrum: μ I = μ II =... = μ n The chemcal potental of the component,, s equal n all present phases. 42 Entropy S ds=0 state functon free Enthalpy G equlbrum dg=0 state varable state varable
43 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 43 startng pont: du = TdS PdV + μdn = P ds = du + dv μdn = T T T = 0 The total system at constant volume conssts of 2 subsystems ( and ). system system n,,,,, V U S T P n, V, U, S, T, P The total system s located n an adabatc contaner. ds = ds + ds du = du and dv = dv and dn = dn
44 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum P ds = du + dv μdn = 0 T T T = wth ds = ds + ds P P 0 = T T T T T T du du dv dv μ dn μ dn = = = = = wth du du and dv dv and dn dn P P μ μ 0 = + T T T T T T thermc equlbrum dv = dn = 0 du dv dn = 0 = du T T T = T 44
45 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 45 P P μ μ 0 = + T T T T T T mechancal du dv dn = equlbrum du dn P P 0 = dv wth T T P = T T materal equlbrum du μ μ 0 = dn wth T = T = T T = = = = dv 0 0 = P μ = μ
46 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 46 du = TdS PdV + μdn = () The drect applcaton of equaton () leads n ths case to problems n calculaton of dn. varable transformaton va ntegraton U = TS PV + μn = exact dfferental du = TdS + SdT PdV VdP + μ dn + n dμ = = comparson of both equaton subtracton of eq. () from eq. (2) (2) 0 = SdT VdP + ndμ = General Gbbs-Duhem equaton
47 dependence on temperature Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum dg = SdT + VdP + μdn = 47 law of Schwarz: z z G G = = r q q r n T T n r q qr P, n PT, PT, Pn, G G μ = μ = n T n T PT, PT, Pn, G G S = S = = s T n T n Pn, Pn, Pn, PT, PT, μ T = P s
48 dependence on temperature Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum alternatve ( μ / T ) dg = SdT + VdP + μdn μ T μ μ T P st = = 2 2 T T T P = 48 G = H TS μ = h Ts Ts μ = h ( μ / T ) T P = h T 2
49 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 49 dependence on pressure dg = SdT + VdP + μdn = z z G G = = r q q r n P P n r q qr T, n PT, PT, Tn, G G μ = μ = n P n P TP, PT, Tn, Tn, G G V = V = = P n P n Tn, Tn, PT, TP, v μ P = T v
50 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 50 0 = sdt vdp + xdμ = general Gbbs-Duhem equaton applcaton to pure substance: 0 = sdt vdp + dμ dμ = sdt + vdp ntegraton at T=const. from reference pressure P 0 to system pressure P μ ( PT, ) P P RT dμ = vdp = dp P μ ( P, T) P P standard term transton term 0 P 0 μ( PT, ) μ( P, T) = RTl n μ( PT, ) μ( P, T) RTln 0 = + P deal gas P P 0
51 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 5 0 = sdt vdp + xdμ = applcaton to pure substances: 0 = sdt vdp + d μ dμ = SdT + VdP μ ( PT, ) dμ = P 0 0 μ ( P, T) P for deal gas vdp μ The chemcal potental of real gas depends on the thermc equaton of state v(t,p). = + P μ( PT, ) μ( P, T) RT ln 0 ( PT, ) μ( P, T) RTln P 0 for real gas: f = fugacty 0 lm f = P P 0 general Gbbs-Duhem equaton ntegraton at T=const. from reference pressure P 0 to system pressure P f P = + 0
52 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 52 for deal gas μ = + P μ( PT, ) μ( P, T) RT ln 0 ( PT, ) μ( P, T) RTln P 0 for real gas: f = Fugacty 0 (Lews) μ f P = + 0 P f P P 0 ( P, T ) = μ( P, T ) + RT ln + RT ln 0 ϕ = f P deal gas ϕ fugacty coeffcent P 0 real gas lmϕ = f μ( PT, ) = μideal ( PT, ) + RTln = μideal ( PT, ) + RTlnϕ P
53 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 53 pure real gas μ P f P P 0 ( P, T ) = μ( P, T ) + RT ln + RT ln 0 f = ϕp real gas n a mxture: deal gas f = ϕ P = ϕ xp real gas ϕ fugacty coeffcent 0 P ϕxp μ( PT,, x) = μ0( P, T) + RTln + RTln 0 P P 0 (,, ) 0(, ) ln P μ PT x = μ P T + RT RTln 0 + ( x) + RTln( ϕ) P deal gas deal mxture real mxture
54 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum chemcal potental of components n lqud mxtures defnton for deal mxtures: 0 μ ( T, P, x ) = μ ( T, P) + RTlnx () 54 The standard potental μ 0 (T,P) s the chemcal potental of the pure component,, at system temperature, T, and system pressure, P. standard state: pure substance Features of deal mxtures: ll mxng quanttes (v E, h E ) of the frst law of thermodynamcs are zero. The chemcal potental can be calculated usng eq. (). Real mxtures: ll mxng quanttes (v E, h E ) of the frst law of thermodynamcs are not zero. Hence, the chemcal potental of eq. () needs a correcton. μ ( T, P, x ) = μ ( T, P) + RTlna a = actvty of substance 0 a = xγ γ = actvty coeffcent of substance
55 Polymer Thermodynamcs 3. Chemcal Potental 3.4. Phase equlbrum 55 μ ( T, P, x ) = μ ( T, P) + RTlnx defnton: 0 The standard potental μ 0 (T,P) s the chemcal potental of the pure component,, at system temperature, T, and system pressure, P. standard state: pure substance applcaton to gas mxture partal pressure P = xp P= P = PV for deal gases: = nrt P μ( T, P) = μ0( T, P) + RTln P
Thermodynamics II. Department of Chemical Engineering. Prof. Kim, Jong Hak
Thermodynamcs II Department of Chemcal Engneerng Prof. Km, Jong Hak Soluton Thermodynamcs : theory Obectve : lay the theoretcal foundaton for applcatons of thermodynamcs to gas mxture and lqud soluton
More informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More information...Thermodynamics. If Clausius Clapeyron fails. l T (v 2 v 1 ) = 0/0 Second order phase transition ( S, v = 0)
If Clausus Clapeyron fals ( ) dp dt pb =...Thermodynamcs l T (v 2 v 1 ) = 0/0 Second order phase transton ( S, v = 0) ( ) dp = c P,1 c P,2 dt Tv(β 1 β 2 ) Two phases ntermngled Ferromagnet (Excess spn-up
More informationa for save as PDF Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities
a for save as PDF Chemstry 163B Introducton to Multcomponent Systems and Partal Molar Quanttes 1 the problem of partal mmolar quanttes mx: 10 moles ethanol C 2 H 5 OH (580 ml) wth 1 mole water H 2 O (18
More informationAppendix II Summary of Important Equations
W. M. Whte Geochemstry Equatons of State: Ideal GasLaw: Coeffcent of Thermal Expanson: Compressblty: Van der Waals Equaton: The Laws of Thermdynamcs: Frst Law: Appendx II Summary of Important Equatons
More informationSolution Thermodynamics
CH2351 Chemcal Engneerng Thermodynamcs II Unt I, II www.msubbu.n Soluton Thermodynamcs www.msubbu.n Dr. M. Subramanan Assocate Professor Department of Chemcal Engneerng Sr Svasubramanya Nadar College of
More informationThermodynamics General
Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons,
More informationEnergy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model
Lecture 4. Thermodynamcs [Ch. 2] Energy, Entropy, and Avalablty Balances Phase Equlbra - Fugactes and actvty coeffcents -K-values Nondeal Thermodynamc Property Models - P-v-T equaton-of-state models -
More informationSupplementary Notes for Chapter 9 Mixture Thermodynamics
Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects
More informationNAME and Section No. it is found that 0.6 mol of O
NAME and Secton No. Chemstry 391 Fall 7 Exam III KEY 1. (3 Ponts) ***Do 5 out of 6***(If 6 are done only the frst 5 wll be graded)*** a). In the reacton 3O O3 t s found that.6 mol of O are consumed. Fnd
More informationIf two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9.
9.9 Real Solutons Exhbt Devatons from Raoult s Law If two volatle and mscble lquds are combned to form a soluton, Raoult s law s not obeyed. Use the expermental data n Table 9.3: Physcal Chemstry 00 Pearson
More informationChapter 3. Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc.
Chapter 3 Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc. Concepts Energy functions F and G Chemical potential, µ Partial Molar properties
More information3. Be able to derive the chemical equilibrium constants from statistical mechanics.
Lecture #17 1 Lecture 17 Objectves: 1. Notaton of chemcal reactons 2. General equlbrum 3. Be able to derve the chemcal equlbrum constants from statstcal mechancs. 4. Identfy how nondeal behavor can be
More informationCHEMICAL REACTIONS AND DIFFUSION
CHEMICAL REACTIONS AND DIFFUSION A.K.A. NETWORK THERMODYNAMICS BACKGROUND Classcal thermodynamcs descrbes equlbrum states. Non-equlbrum thermodynamcs descrbes steady states. Network thermodynamcs descrbes
More informationNAME and Section No.
Chemstry 391 Fall 2007 Exam I KEY (Monday September 17) 1. (25 Ponts) ***Do 5 out of 6***(If 6 are done only the frst 5 wll be graded)*** a). Defne the terms: open system, closed system and solated system
More informationEffect of adding an ideal inert gas, M
Effect of adding an ideal inert gas, M Add gas M If there is no change in volume, then the partial pressures of each of the ideal gas components remains unchanged by the addition of M. If the reaction
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationName: SID: Discussion Session:
Name: SID: Dscusson Sesson: Chemcal Engneerng Thermodynamcs 141 -- Fall 007 Thursday, November 15, 007 Mdterm II SOLUTIONS - 70 mnutes 110 Ponts Total Closed Book and Notes (0 ponts) 1. Evaluate whether
More informationV T for n & P = constant
Pchem 365: hermodynamcs -SUMMARY- Uwe Burghaus, Fargo, 5 9 Mnmum requrements for underneath of your pllow. However, wrte your own summary! You need to know the story behnd the equatons : Pressure : olume
More informationChapter 18, Part 1. Fundamentals of Atmospheric Modeling
Overhead Sldes for Chapter 18, Part 1 of Fundamentals of Atmospherc Modelng by Mark Z. Jacobson Department of Cvl & Envronmental Engneerng Stanford Unversty Stanford, CA 94305-4020 January 30, 2002 Types
More informationReview of Classical Thermodynamics
Revew of Classcal hermodynamcs Physcs 4362, Lecture #1, 2 Syllabus What s hermodynamcs? 1 [A law] s more mpressve the greater the smplcty of ts premses, the more dfferent are the knds of thngs t relates,
More informationIntroduction to Statistical Methods
Introducton to Statstcal Methods Physcs 4362, Lecture #3 hermodynamcs Classcal Statstcal Knetc heory Classcal hermodynamcs Macroscopc approach General propertes of the system Macroscopc varables 1 hermodynamc
More informationChemical Equilibrium. Chapter 6 Spontaneity of Reactive Mixtures (gases) Taking into account there are many types of work that a sysem can perform
Ths chapter deals wth chemcal reactons (system) wth lttle or no consderaton on the surroundngs. Chemcal Equlbrum Chapter 6 Spontanety of eactve Mxtures (gases) eactants generatng products would proceed
More informationSolution Thermodynamics
Soluton hermodynamcs usng Wagner Notaton by Stanley. Howard Department of aterals and etallurgcal Engneerng South Dakota School of nes and echnology Rapd Cty, SD 57701 January 7, 001 Soluton hermodynamcs
More information4.2 Chemical Driving Force
4.2. CHEMICL DRIVING FORCE 103 4.2 Chemcal Drvng Force second effect of a chemcal concentraton gradent on dffuson s to change the nature of the drvng force. Ths s because dffuson changes the bondng n a
More informationLecture 2 Grand Canonical Ensemble GCE
Lecture 2 Grand Canoncal Ensemble GCE 2.1 hermodynamc Functons Contnung on from last day we also note that thus, dω = df dµ µd = Sd P dv dµ (2.1) P = V = S = From the expresson for the entropy, we therefore
More informationPhysics 607 Exam 1. ( ) = 1, Γ( z +1) = zγ( z) x n e x2 dx = 1. e x2
Physcs 607 Exam 1 Please be well-organzed, and show all sgnfcant steps clearly n all problems. You are graded on your wor, so please do not just wrte down answers wth no explanaton! Do all your wor on
More informationA Self-Consistent Gibbs Excess Mixing Rule for Cubic Equations of State: derivation and fugacity coefficients
A Self-Consstent Gbbs Excess Mxng Rule for Cubc Equatons of State: dervaton and fugacty coeffcents Paula B. Staudt, Rafael de P. Soares Departamento de Engenhara Químca, Escola de Engenhara, Unversdade
More information3) Thermodynamic equation to characterize interfaces
3) Thermodynamc equaton to characterze nterfaces 3.1) Gbbs Model Realty: rapd contnuous change of chemcal and thermodynamc propertes Replaced by model (constant propertes up to the surface) uv bulk uv
More informationChapter 5. Simple Mixtures Fall Semester Physical Chemistry 1 (CHM2201)
Chapter 5. Simple Mixtures 2011 Fall Semester Physical Chemistry 1 (CHM2201) Contents The thermodynamic description of mixtures 5.1 Partial molar quantities 5.2 The thermodynamic of Mixing 5.3 The chemical
More informationUniversity of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014
Lecture 16 8/4/14 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 214. Real Vapors and Fugacty Henry s Law accounts or the propertes o extremely dlute soluton. s shown n Fgure
More informationAssignment 4. Adsorption Isotherms
Insttute of Process Engneerng Assgnment 4. Adsorpton Isotherms Part A: Compettve adsorpton of methane and ethane In large scale adsorpton processes, more than one compound from a mxture of gases get adsorbed,
More informationUniversity of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014
Lecture 12 7/25/14 ERD: 7.1-7.5 Devoe: 8.1.1-8.1.2, 8.2.1-8.2.3, 8.4.1-8.4.3 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 2014 A. Free Energy and Changes n Composton: The
More informationI wish to publish my paper on The International Journal of Thermophysics. A Practical Method to Calculate Partial Properties from Equation of State
I wsh to publsh my paper on The Internatonal Journal of Thermophyscs. Ttle: A Practcal Method to Calculate Partal Propertes from Equaton of State Authors: Ryo Akasaka (correspondng author) 1 and Takehro
More informationand Statistical Mechanics Material Properties
Statstcal Mechancs and Materal Propertes By Kuno TAKAHASHI Tokyo Insttute of Technology, Tokyo 15-855, JAPA Phone/Fax +81-3-5734-3915 takahak@de.ttech.ac.jp http://www.de.ttech.ac.jp/~kt-lab/ Only for
More informationChemistry 163B Free Energy and Equilibrium E&R ( ch 6)
Chemstry 163B Free Energy and Equlbrum E&R ( ch 6) 1 ΔG reacton and equlbrum (frst pass) 1. ΔG < spontaneous ( natural, rreversble) ΔG = equlbrum (reversble) ΔG > spontaneous n reverse drecton. ΔG = ΔHΔS
More informationIrreversibility of Processes in Closed System
Unversty of Segen Insttute of Flud- & hermodynamcs 5 2/1 Irreversblty of Processes n Closed System m G 2 m c 2 2, p, V m g h h 1 mc 1 1 p, p, V G J.P. Joule Strrng experment v J.B. Fourer Heat transfer
More informationThe ChemSep Book. Harry A. Kooijman Consultant. Ross Taylor Clarkson University, Potsdam, New York University of Twente, Enschede, The Netherlands
The ChemSep Book Harry A. Koojman Consultant Ross Taylor Clarkson Unversty, Potsdam, New York Unversty of Twente, Enschede, The Netherlands Lbr Books on Demand www.bod.de Copyrght c 2000 by H.A. Koojman
More informationTP A SOLUTION. For an ideal monatomic gas U=3/2nRT, Since the process is at constant pressure Q = C. giving ) =1000/(5/2*8.31*10)
T A SOLUTION For an deal monatomc gas U/nRT, Snce the process s at constant pressure Q C pn T gvng a: n Q /( 5 / R T ) /(5/*8.*) C V / R and C / R + R 5 / R. U U / nr T (/ ) R T ( Q / 5 / R T ) Q / 5 Q
More informationNon-Ideality Through Fugacity and Activity
Non-Idealty Through Fugacty and Actvty S. Patel Deartment of Chemstry and Bochemstry, Unversty of Delaware, Newark, Delaware 19716, USA Corresondng author. E-mal: saatel@udel.edu 1 I. FUGACITY In ths dscusson,
More information#64. ΔS for Isothermal Mixing of Ideal Gases
#64 Carnot Heat Engne ΔS for Isothermal Mxng of Ideal Gases ds = S dt + S T V V S = P V T T V PV = nrt, P T ds = v T = nr V dv V nr V V = nrln V V = - nrln V V ΔS ΔS ΔS for Isothermal Mxng for Ideal Gases
More informationThe Euler Equation. Using the additive property of the internal energy U, we can derive a useful thermodynamic relation the Euler equation.
The Euler Equation Using the additive property of the internal energy U, we can derive a useful thermodynamic relation the Euler equation. Let us differentiate this extensivity condition with respect to
More informationGeneral Thermodynamics for Process Simulation. Dr. Jungho Cho, Professor Department of Chemical Engineering Dong Yang University
General Thermodynamcs for Process Smulaton Dr. Jungho Cho, Professor Department of Chemcal Engneerng Dong Yang Unversty Four Crtera for Equlbra μ = μ v Stuaton α T = T β α β P = P l μ = μ l1 l 2 Thermal
More informationIntroduction to Interfacial Segregation. Xiaozhe Zhang 10/02/2015
Introducton to Interfacal Segregaton Xaozhe Zhang 10/02/2015 Interfacal egregaton Segregaton n materal refer to the enrchment of a materal conttuent at a free urface or an nternal nterface of a materal.
More informationChapter One Mixture of Ideal Gases
herodynacs II AA Chapter One Mxture of Ideal Gases. Coposton of a Gas Mxture: Mass and Mole Fractons o deterne the propertes of a xture, we need to now the coposton of the xture as well as the propertes
More informationSome properties of the Helmholtz free energy
Some properties of the Helmholtz free energy Energy slope is T U(S, ) From the properties of U vs S, it is clear that the Helmholtz free energy is always algebraically less than the internal energy U.
More informationOsmotic pressure and protein binding
Osmotc pressure and proten bndng Igor R. Kuznetsov, KochLab Symposum talk 5/15/09 Today we take a closer look at one of the soluton thermodynamcs key ponts from Steve s presentaton. Here t s: d[ln(k off
More informationy i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem
SOLUTION TO HOMEWORK #7 #roblem 1 10.1-1 a. In order to solve ths problem, we need to know what happens at the bubble pont; at ths pont, the frst bubble s formed, so we can assume that all of the number
More information4) It is a state function because enthalpy(h), entropy(s) and temperature (T) are state functions.
Chemical Thermodynamics S.Y.BSc. Concept of Gibb s free energy and Helmholtz free energy a) Gibb s free energy: 1) It was introduced by J.Willard Gibb s to account for the work of expansion due to volume
More informationMME 2010 METALLURGICAL THERMODYNAMICS II. Partial Properties of Solutions
MME 2010 METALLURGICAL THERMODYNAMICS II Partial Properties of Solutions A total property of a system consisting of multiple substances is represented as nm = n i M i If the system consists of a liquid
More information( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.
Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.
More informationA quote of the week (or camel of the week): There is no expedience to which a man will not go to avoid the labor of thinking. Thomas A.
A quote of the week (or camel of the week): here s no expedence to whch a man wll not go to avod the labor of thnkng. homas A. Edson Hess law. Algorthm S Select a reacton, possbly contanng specfc compounds
More informationChapter 13. Gas Mixtures. Study Guide in PowerPoint. Thermodynamics: An Engineering Approach, 5th edition by Yunus A. Çengel and Michael A.
Chapter 3 Gas Mxtures Study Gude n PowerPont to accopany Therodynacs: An Engneerng Approach, 5th edton by Yunus A. Çengel and Mchael A. Boles The dscussons n ths chapter are restrcted to nonreactve deal-gas
More informationTEST 5 (phy 240) 2. Show that the volume coefficient of thermal expansion for an ideal gas at constant pressure is temperature dependent and given by
ES 5 (phy 40). a) Wrte the zeroth law o thermodynamcs. b) What s thermal conductvty? c) Identyng all es, draw schematcally a P dagram o the arnot cycle. d) What s the ecency o an engne and what s the coecent
More informationComputation of Phase Equilibrium and Phase Envelopes
Downloaded from orbt.dtu.dk on: Sep 24, 2018 Computaton of Phase Equlbrum and Phase Envelopes Rtschel, Tobas Kasper Skovborg; Jørgensen, John Bagterp Publcaton date: 2017 Document Verson Publsher's PDF,
More informationChapters 18 & 19: Themodynamics review. All macroscopic (i.e., human scale) quantities must ultimately be explained on the microscopic scale.
Chapters 18 & 19: Themodynamcs revew ll macroscopc (.e., human scale) quanttes must ultmately be explaned on the mcroscopc scale. Chapter 18: Thermodynamcs Thermodynamcs s the study o the thermal energy
More informationMass Transfer Processes
Mass Transfer Processes S. Majd Hassanzadeh Department of Earth Scences Faculty of Geoscences Utrecht Unversty Outlne: 1. Measures of Concentraton 2. Volatlzaton and Dssoluton 3. Adsorpton Processes 4.
More informationProcess Modeling. Improving or understanding chemical process operation is a major objective for developing a dynamic process model
Process Modelng Improvng or understandng chemcal process operaton s a major objectve for developng a dynamc process model Balance equatons Steady-state balance equatons mass or energy mass or energy enterng
More informationMore on phase diagram, chemical potential, and mixing
More on phase diagram, chemical potential, and mixing Narayanan Kurur Department of Chemistry IIT Delhi 13 July 2013 Melting point changes with P ( ) Gα P T = V α V > 0 = G α when P Intersection point
More informationEnvr 210, Chapter 3, Intermolecular forces and partitioning Free energies and equilibrium partitioning chemical potential fugacity activity coef.
Envr 20, Chapter 3, Intermolecular forces and parttonng Free energes and equlbrum parttonng chemcal potental fugacty actvty coef. phase transfer- actvty coef and fugactes more on free energes and equlbrum
More informationA Modulated Hydrothermal (MHT) Approach for the Facile. Synthesis of UiO-66-Type MOFs
Supplementary Informaton A Modulated Hydrothermal (MHT) Approach for the Facle Synthess of UO-66-Type MOFs Zhgang Hu, Yongwu Peng, Zx Kang, Yuhong Qan, and Dan Zhao * Department of Chemcal and Bomolecular
More informationmodeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products
modelng of equlbrum and dynamc mult-component adsorpton n a two-layered fxed bed for purfcaton of hydrogen from methane reformng products Mohammad A. Ebrahm, Mahmood R. G. Arsalan, Shohreh Fatem * Laboratory
More informationNot at Steady State! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Yes! Class 15. Is the following possible?
Chapter 5-6 (where we are gong) Ideal gae and lqud (today) Dente Partal preure Non-deal gae (next tme) Eqn. of tate Reduced preure and temperature Compreblty chart (z) Vapor-lqud ytem (Ch. 6) Vapor preure
More informationGasometric Determination of NaHCO 3 in a Mixture
60 50 40 0 0 5 15 25 35 40 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g)
More informationThermodynamics. Section 4
Secton 4 Thermodynamcs Hendrck C. Van Ness, D.Eng., Howard. Isermann Department of Chemcal Engneerng, Rensselaer olytechnc Insttute; Fellow, Amercan Insttute of Chemcal Engneers; Member, Amercan Chemcal
More informationPART I: MULTIPLE CHOICE (32 questions, each multiple choice question has a 2-point value, 64 points total).
CHEMISTRY 123-07 Mdterm #2 answer key November 04, 2010 Statstcs: Average: 68 p (68%); Hghest: 91 p (91%); Lowest: 37 p (37%) Number of students performng at or above average: 58 (53%) Number of students
More informationElectrochemical Equilibrium Electromotive Force
CHM465/865, 24-3, Lecture 5-7, 2 th Sep., 24 lectrochemcal qulbrum lectromotve Force Relaton between chemcal and electrc drvng forces lectrochemcal system at constant T and p: consder Gbbs free energy
More information(1) The saturation vapor pressure as a function of temperature, often given by the Antoine equation:
CE304, Sprng 2004 Lecture 22 Lecture 22: Topcs n Phase Equlbra, part : For the remander of the course, we wll return to the subject of vapor/lqud equlbrum and ntroduce other phase equlbrum calculatons
More informationMS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7
2017 Spring Semester MS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7 Byungha Shin ( 신병하 ) Dept. of MSE, KAIST Largely based on lecture notes of Prof. Hyuck-Mo Lee and Prof. WooChul
More informationChapter 3 Thermochemistry of Fuel Air Mixtures
Chapter 3 Thermochemstry of Fuel Ar Mxtures 3-1 Thermochemstry 3- Ideal Gas Model 3-3 Composton of Ar and Fuels 3-4 Combuston Stochometry t 3-5 The1 st Law of Thermodynamcs and Combuston 3-6 Thermal converson
More informationChemistry. Lecture 10 Maxwell Relations. NC State University
Chemistry Lecture 10 Maxwell Relations NC State University Thermodynamic state functions expressed in differential form We have seen that the internal energy is conserved and depends on mechanical (dw)
More informationCHEMICAL ENGINEERING
Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1 TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton
More informationLNG CARGO TRANSFER CALCULATION METHODS AND ROUNDING-OFFS
CARGO TRANSFER CALCULATION METHODS AND ROUNDING-OFFS CONTENTS 1. Method for determnng transferred energy durng cargo transfer. Calculatng the transferred energy.1 Calculatng the gross transferred energy.1.1
More informationThermodynamic Variables and Relations
MME 231: Lecture 10 Thermodynamic Variables and Relations A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Thermodynamic relations derived from the Laws of Thermodynamics Definitions
More informationEquation of State Modeling of Phase Equilibrium in the Low-Density Polyethylene Process
Equaton of State Modelng of Phase Equlbrum n the Low-Densty Polyethylene Process H. Orbey, C. P. Boks, and C. C. Chen Ind. Eng. Chem. Res. 1998, 37, 4481-4491 Yong Soo Km Thermodynamcs & Propertes Lab.
More informationapplied to a single-phase fluid in a closed system wherein no chemical reactions occur.
The basc relaton connectng the Gbbs energy to the temperature and pressure n any closed system: (ng) (ng) d(ng) d dt (nv)d (ns)dt T T,n appled to a sngle-phase flud n a closed system wheren no chemcal
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationName ID # For relatively dilute aqueous solutions the molality and molarity are approximately equal.
Name ID # 1 CHEMISTRY 212, Lect. Sect. 002 Dr. G. L. Roberts Exam #1/Sprng 2000 Thursday, February 24, 2000 CLOSED BOOK EXM No notes or books allowed. Calculators may be used. tomc masses of nterest are
More informationThermodynamics and statistical mechanics in materials modelling II
Course MP3 Lecture 8/11/006 (JAE) Course MP3 Lecture 8/11/006 Thermodynamcs and statstcal mechancs n materals modellng II A bref résumé of the physcal concepts used n materals modellng Dr James Ellott.1
More information10.40 Appendix Connection to Thermodynamics and Derivation of Boltzmann Distribution
10.40 Appendx Connecton to Thermodynamcs Dervaton of Boltzmann Dstrbuton Bernhardt L. Trout Outlne Cannoncal ensemble Maxmumtermmethod Most probable dstrbuton Ensembles contnued: Canoncal, Mcrocanoncal,
More informationEstimation of the composition of the liquid and vapor streams exiting a flash unit with a supercritical component
Department of Energ oltecnco d Mlano Va Lambruschn - 05 MILANO Eercses of Fundamentals of Chemcal rocesses rof. Ganpero Gropp Eercse 8 Estmaton of the composton of the lqud and vapor streams etng a unt
More informationCinChE Problem-Solving Strategy Chapter 4 Development of a Mathematical Model. formulation. procedure
nhe roblem-solvng Strategy hapter 4 Transformaton rocess onceptual Model formulaton procedure Mathematcal Model The mathematcal model s an abstracton that represents the engneerng phenomena occurrng n
More informationBe true to your work, your word, and your friend.
Chemstry 13 NT Be true to your work, your word, and your frend. Henry Davd Thoreau 1 Chem 13 NT Chemcal Equlbrum Module Usng the Equlbrum Constant Interpretng the Equlbrum Constant Predctng the Drecton
More informationPhysics 240: Worksheet 30 Name:
(1) One mole of an deal monatomc gas doubles ts temperature and doubles ts volume. What s the change n entropy of the gas? () 1 kg of ce at 0 0 C melts to become water at 0 0 C. What s the change n entropy
More informationExercises of Fundamentals of Chemical Processes
Department of Energ Poltecnco d Mlano a Lambruschn 4 2056 MILANO Exercses of undamentals of Chemcal Processes Prof. Ganpero Gropp Exercse 7 ) Estmaton of the composton of the streams at the ext of an sothermal
More informationPh.D. Qualifying Examination in Kinetics and Reactor Design
Knetcs and Reactor Desgn Ph.D.Qualfyng Examnaton January 2006 Instructons Ph.D. Qualfyng Examnaton n Knetcs and Reactor Desgn January 2006 Unversty of Texas at Austn Department of Chemcal Engneerng 1.
More informationThermodynamics of phase transitions
Thermodynamics of phase transitions Katarzyna Sznajd-Weron Department of Theoretical of Physics Wroc law University of Science and Technology, Poland March 12, 2017 Katarzyna Sznajd-Weron (WUST) Thermodynamics
More informationPETE 310 Lectures # 24 & 25 Chapter 12 Gas Liquid Equilibrium
ETE 30 Lectures # 24 & 25 Chapter 2 Gas Lqud Equlbrum Thermal Equlbrum Object A hgh T, Object B low T Intal contact tme Intermedate tme. Later tme Mechancal Equlbrum ressure essels Vale Closed Vale Open
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationLecture 8. Chapter 7. - Thermodynamic Web - Departure Functions - Review Equations of state (chapter 4, briefly)
Lecture 8 Chapter 5 - Thermodynamc Web - Departure Functons - Revew Equatons of state (chapter 4, brefly) Chapter 6 - Equlbrum (chemcal potental) * Pure Component * Mxtures Chapter 7 - Fugacty (chemcal
More information1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v. lnt + RlnV + cons tant
1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v lnt + RlnV + cons tant (1) p, V, T change Reversible isothermal process (const. T) TdS=du-!W"!S = # "Q r = Q r T T Q r = $W = # pdv =
More informationPhysics 181. Particle Systems
Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system
More informationPhase equilibria Introduction General equilibrium conditions
.5 hase equlbra.5. Introducton A gven amount of matter (usually called a system) can be characterzed by unform ntensve propertes n ts whole volume or only n some of ts parts; a porton of matter wth unform
More informationNo! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Survey Results. Class 15. Is the following possible?
Survey Reult Chapter 5-6 (where we are gong) % of Student 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Hour Spent on ChE 273 1-2 3-4 5-6 7-8 9-10 11+ Hour/Week 2008 2009 2010 2011 2012 2013 2014 2015 2017 F17
More informationThe Standard Gibbs Energy Change, G
The Standard Gibbs Energy Change, G S univ = S surr + S sys S univ = H sys + S sys T S univ = H sys TS sys G sys = H sys TS sys Spontaneous reaction: S univ >0 G sys < 0 More observations on G and Gº I.
More informationInfluence Of Operating Conditions To The Effectiveness Of Extractive Distillation Columns
Influence Of Operatng Condtons To The Effectveness Of Extractve Dstllaton Columns N.A. Vyazmna Moscov State Unversty Of Envrnmental Engneerng, Department Of Chemcal Engneerng Ul. Staraya Basmannaya 21/4,
More informationChapter 12 Lyes KADEM [Thermodynamics II] 2007
Chapter 2 Lyes KDEM [Therodynacs II] 2007 Gas Mxtures In ths chapter we wll develop ethods for deternng therodynac propertes of a xture n order to apply the frst law to systes nvolvng xtures. Ths wll be
More informationUniversity of Washington Department of Chemistry Chemistry 453 Winter Quarter 2015
Lecture 2. 1/07/15-1/09/15 Unversty of Washngton Department of Chemstry Chemstry 453 Wnter Quarter 2015 We are not talkng about truth. We are talkng about somethng that seems lke truth. The truth we want
More informationPHY688, Statistical Mechanics
Department of Physcs & Astronomy 449 ESS Bldg. Stony Brook Unversty January 31, 2017 Nuclear Astrophyscs James.Lattmer@Stonybrook.edu Thermodynamcs Internal Energy Densty and Frst Law: ε = E V = Ts P +
More informationThermodynamics of Materials
Thermdynamcs f Materals 14th Lecture 007. 4. 8 (Mnday) FUGACITY dg = Vd SdT dg = Vd at cnstant T Fr an deal gas dg = (RT/)d = RT dln Ths s true fr deal gases nly, but t wuld be nce t have a smlar frm fr
More information