MBN 305 Phase Diagrams & Transformations

Transcription

1 MBN 35 Phase Diagrams & ransfrmatins Dr. Ersin Emre Oren Department f Bimedical Engineering Department f Materials Science & Nantechnlgy Engineering OBB University f Ecnmics and echnlgy Ankara - URKEY Binandesign Labratry eeren@etu.edu.tr

2 he Secnd Law f hermdynamics: Irreversibility Questin Pitzer and Culter (J. Amer. Chem. Sc., 6, 3, (938)) have prvided the fllwing data fr the heat capacity f Na SO 4. Calculate the entrpy f Na SO 4 at K. (K) C p (J/mle.K) = = cp S S S d cp S = S+ d S = c p d c p 6 c p.6 Cp 4 Cp.4 f( x). S = = c p d 43.4 J/mle.K , x

3 Pressure

4 Entrpy Changes in Reversible Prcesses ds Q = i. Reversible Adiabatic Prcess: Q r = ds = ii. Reversible Isthermal Prcess: Q r V R ln = V ds R ln V = V iii. Reversible Ischric Prcess: Qr = cvd iv. Reversible Isbaric Prcess: Qr = cpd cv ln ds = d = cv cp ln ds = d = cp iv. Reversible Isbaric Prcess: Q =H r m ds m = S = H m

5 Entrpy des nt change in reversible adiabatic prcess thus we als call this type f prcesses isentrpic. ds = Entrpy Changes in sme Irreversible Prcesses Hwever entrpy can change in irreversible adiabatic prcess. ds Q i. Adiabatic free expansin f an ideal gas: ( P, V, ) ( P, V, ) Q = P ( P, V, ) ( P V ),, x ds R ln V = V ( P, V, ) ds R ln V = V V

6 Questin Calculate the entrpy change f the system when supercled liquid Ag is slidified at 93 C at cnstant P. m = 96.5 C liquid c p = 3.5 J/mle.K C slid p H m = 9 J/mle 3 5 c =.3 + (8.54 ) + (.5 ) C Ag l Ag l Ag Ag s C % ransfrmed Irreversible phase transfrmatin Questin Calculate the entrpy change f the universe when supercled liquid Ag is slidified at 93 C at cnstant P. Questin Calculate the Gibbs Free energy change when supercled liquid Ag is slidified at 93 C at cnstant P.

7 Questin Let us calculate the entrpy increase fr an isthermal expansin f ideal gas frm V t V. S Q du = Q W du V Q = W = PdV V V Q = nr dv V V Q nr ln V = V S nr ln V = V V ln Smle = R V V ln Smlecule = k V R = 8.34 J/K.ml 3 k =.386 J/K

8 MBN 35 Phase Diagrams & ransfrmatins hery f Slutins Dr. Ersin Emre Oren Department f Bimedical Engineering Department f Materials Science & Nantechnlgy Engineering OBB University f Ecnmics and echnlgy Ankara - URKEY Binandesign Labratry eeren@etu.edu.tr

9 Equilibrium Mechanical hermal Chemical hermdynamic Equilibrium Chemical Equilibrium Internal Energy depends n the quantity f matter in the system du Mixing Energy independent f the amunt f matter present ds Mixing: systems tend t mve twards a mre prbable state. dg = du ds S kln W = W

10 Equilibrium Cncentratin f Defects in Crystals mle f Ge single crystal + Ga impurities: dg = du ds Pure/perfect Ge crystal: G N is the # f lattice cites. Internal Energy When we substitude Ga atm instead f Ge atm: When we substitude n Ga atm instead f n Ge atm: UGa Ge U = n UGa Ge face-centered diamnd-cubic Mixing Energy State f crystal Pure/perfect Ga atm: Ga atm: 3 Ga atm: n Ga atm: Randmness N ( ) N N ( )( ) 3 N N N N! n! ( N n)! Mixing Entrpy: N! n! ( N n)! N! S = k ln = k ln n! ( N n)! Mixing Energy: N! Umixing = k ln n! ( N n)!

11 Equilibrium Cncentratin f Defects in Crystals G = G G N! G( n) = G + n UGa Ge k ln n! ( N n)! gamma functin tn n! = ( n + ) = e t equilibrium: d Gn ( ) = dn d N G( n) = UGa Ge k ln = dn n k N ln = U n Ga Ge k ln n N = U Ga Ge U n( ) = N exp i k

12 Equilibrium Cncentratin f Defects in Crystals G = G G N! G( n) = G + n UGa Ge k ln n! ( N n)! 5 = K G( n, ) Gn ( ) 4 G( n,.5) 3 G( n, ) G( n, 3) G( n, 5) < < 3 < n n n =?

13 Next Lecture: We will cntinue with the HEORY OF SOLUIONS tpic!