Physical chemistr Physical Chemistry Cheng Xuan February 2004, Spring Semester
Physical Chemistry Cheng Xuan February 2004, Spring Semester Physical Chemistry
Physical Chemistry Material Equilibrium Review from the last class → Basic equations du tds- pdv closed syst, rev. proc., P-v (425)* work only H≡U+PV (426) A≡U-Ts (427)* G≡H-Ts U closed syst in equi lib., P-v aT work only (4.29) OH closed syst., in equi lib., P-v P aT ly (4.30) P aS aS OT ar/closed syst., in equilib.(4.31)* P
Physical Chemistry Review from the last class Material Equilibrium Basic Equations H U + PV (4.26)* A U – TS (4.27)* G H - TS (4.28)* dU = TdS - PdV (4.25)* closed syst., rev. proc., P-V work only V V T U C = (4.29)* closed syst., in equilib., P-V work only P P T H C = (4.30)* closed syst., in equilib., P-V work only V V T S C T = P P T S C T = closed syst., in equilib. (4.31)*
Physical Chemistry Material Equilibrium Review from the last class H H=U+pv U G=H-TS TS G FA+pv TS pV A=U-TS Relations among different functions
Physical Chemistry Review from the last class Material Equilibrium Relations among different functions
Physical Chemistry Material Equilibrium The Gibbs equations du e tds- pdv (4.33)2 dh = tas t vdP closed syst, rev 4.34) proc., P-v work da=-sdT- Pdv only (4.35) dg=-sdt+ vdp. (4.36)
The Gibbs Equations Physical Chemistry Material Equilibrium dG = -SdT + VdP (4.36)* dA = -SdT - PdV (4.35) dH = TdS + VdP (4.34) dU = TdS - PdV (4.33)* closed syst., rev. proc., P-V work only
Physical Chemistry Material Equilibrium aM aN、02za ON Oy croy axa du e tds- pdv S dh= tds t vdP aP S a示 P C da=-sdt- pdv dg=-sdt+ dP T P
Physical Chemistry Material Equilibrium dG = -SdT + VdP dA = -SdT - PdV dH = TdS + VdP dU = TdS - PdV S S P V P T = V V S T S P = − T T V P V S = T T P V P S = − ( ) ( ) x y M N y x = 2 2 ( ) , ( ) x y M z N z y x y x x y = =
Physical Chemistry Material Equilibrium Maxwell relations a丿( (4.44) C as( ap C aP (4.45) T T
Maxwell Relations T T V P V S = T T P V P S = − (4.45) S S P V P T = V V S T S P = − (4.44) Physical Chemistry Material Equilibrium
Physical Chemistry Material Equilibrium Isobaric thermalexpansivit 1(oⅣ a(1,P) (1.43) VaT P Isothermal compressibility (4.39) 1(a K(T, P) (1.4) V aP 2 C (453) K aT JT (a-1)(452) aP (264)*1m H P
T P V V T P 1 ( , ) P T V V T P − 1 ( , ) (4.39)* Isobaric thermal expansivity Physical Chemistry Material Equilibrium Isothermal compressibility (1.43)* (1.44)* (4.53) 2 TV CP −CV = ( −1) = T C V P JT (4.52) H JT P T (2.64)*
Physical Chemistry Material Equilibrium Application of Maxwell Relations Example 1: Prove that the internal energy of ideal gas is a function of temperature only Answers. du=tds-Pdr O S b For ideal gas PV=nRT P=nRT aP nR aT aU aP nR P P=0 aT
Application of Maxwell Relations V nRT PV = nRT P = Physical Chemistry Material Equilibrium Example 1: Prove that the internal energy of ideal gas is a function of temperature only. Answers. For ideal gas V nR T P V = P T P T V U T V − = P V nR = T − = 0 dU =TdS −PdVP V S T V U T T − = T T V P V S =
Physical Chemistry Material Equilibrium Application of Maxwell Relations Example 2: Calculate 4U when an ideal gas changes from PI,V, T, to P2,2, T2 (Hint: applying/ou Answers U=U(7,V) aU aP P aT aU T+aU aT aP dT+ P ldv aT △U=∫Gd+ aP P aT
Physical Chemistry Material Equilibrium Application of Maxwell Relations Example 2: Calculate U when an ideal gas changes from P1 , V1 , T1 to P2 , V2 , T2 . (Hint: applying ) V T U U U T V = ( , ) Answers. dV V U dT T U dU V T + = P dV T P C dT T V V − = + P dV T P U C dT T V V − = + P T P T V U T V − =
Physical Chemistry Material Equilibrium e Chapter 4 Material Equilibrium Calculation of changes in state functions ● Calculation of as aS dT+ dP OT' aP PdT-avdP(4.59) aS (449) P O(4.50 aT TaP OT' △S=S2-S dT-aldP (460
(4.59) Calculation of S dT VdP T C dP P S dT T S dS P P T = − + = Calculation of changes in state functions = − = − 2 1 2 1 2 1 dT VdP T C S S S P (4.60) V T V P S T P = − = − (4.50) T C T S P P = (4.49) Physical Chemistry Chapter 4 Material Equilibrium Material Equilibrium
