Thermodynamics Gibbs Free Energy ByeongJoo Lee Enthalpy POSTECH
Thermodynamics Gibbs Free Energy, Byeong-Joo Lee Enthalpy, … POSTECH - MSE calphad@postech. ac. kr Byeong-Joo Lee http: //cmse. postech. ac. kr
Gibbs Energy for a Unary System - from d. G = –Sd. T + Vd. P Gibbs Energy as a function of T and P @ constant T Byeong-Joo Lee http: //cmse. postech. ac. kr
Gibbs Energy for a Unary System - from G = H – ST Gibbs Energy as a function of T and P @ constant T Byeong-Joo Lee http: //cmse. postech. ac. kr
Gibbs Energy for a Unary System - Temperature Dependency 서로 다른 출발점에서 유도된 위의 두 식은 같은 식인가? Empirical Representation of Heat Capacities 를 이용하여 위의 두 식이 동일한 것임을 증명하라. Byeong-Joo Lee http: //cmse. postech. ac. kr
Gibbs Energy for a Unary System - Effect of Pressure Molar volume of Fe Expansivity = 7. 1 cm 3 = 0. 3 × 10 -4 K-1 ∆H(1→ 100 atm, 298) = 17 cal ※ The same enthalpy increase is obtained by heating from 298 to 301 K at 1 atm Molar volume of Al Expansivity = 10 cm 3 = 0. 69 × 10 -4 K-1 ∆H(1→ 100 atm, 298) = 23. 7 cal ※ The same enthalpy increase is obtained by heating from 298 to 302 K at 1 atm ∆S(1→ 100 atm, 298) = -0. 00052 e. u. for Fe -0. 00167 e. u. for Al ※ The same entropy decrease is obtained by lowering the temperature from 298 by 0. 27 and 0. 09 K at 1 atm. ※ The molar enthalpies and entropies of condensed phases are relatively insensitive to pressure change Byeong-Joo Lee http: //cmse. postech. ac. kr
Gibbs Energy for a Unary System - absolute value available ? • V(T, P) based on expansivity and compressibility • Cp(T) • S 298: by integrating Cp/T from 0 to 298 K and using 3 rd law of thermodynamics (the entropy of any homogeneous substance in complete internal equilibrium may be taken as zero at 0 K) • H 298: from first principles calculations, but generally unknown ※ H 298 becomes a reference value for GT ※ Introduction of Standard State Byeong-Joo Lee http: //cmse. postech. ac. kr
Temperature and Pressure Dependence of Molar Volume of Fe Byeong-Joo Lee http: //cmse. postech. ac. kr
Temperature dependence of Specific Heat of Fe Byeong-Joo Lee http: //cmse. postech. ac. kr
Temperature dependence of molar Enthalpy of Fe Byeong-Joo Lee http: //cmse. postech. ac. kr
Byeong-Joo Lee http: //cmse. postech. ac. kr
Gibbs Energy change of a reaction • Neumann-Kopp rule: heat capacity of a solid compound is equal to the sum of the heat capacities of its constituent elements. • Richards’ rule: • Trouton’s rule: cal/degree In reactions in which a gas reacts with a condensed phase to produce a condensed phase, the entropy change is that corresponding to the disappearance of the gas. Byeong-Joo Lee http: //cmse. postech. ac. kr
First Approximations Richards’ rule: cal/degree Trouton’s rule: cal/degree Byeong-Joo Lee http: //cmse. postech. ac. kr
Numerical Example • A quantity of supercooled liquid Tin is adiabatically contained at 495 K. Calculate the fraction of the Tin which spontaneously freezes. Given J at Tm = 505 K 495 K 1 mole of liquid x moles of solid (1 -x) moles of liquid Byeong-Joo Lee http: //cmse. postech. ac. kr
Byeong-Joo Lee http: //cmse. postech. ac. kr
First Law of thermodynamics Microscopic vs. Macroscopic View Point의 이해 State function vs. Process variable, 기타 용어의 이해 열역학 1법칙의 탄생 과정, 1법칙 중요성의 이해 Special processes의 중요성 이해, 응용력 1. 2. 3. 4. Constant-Volume Process: ΔU ＝ qv Constant-Pressure Process: ΔH ＝ qp Reversible Adiabatic Process: q ＝ 0 Reversible Isothermal Process: ΔU ＝ ΔH ＝ 0 Byeong-Joo Lee http: //cmse. postech. ac. kr
Second Law of thermodynamics (Mechanical, Thermal, Chemical) Irreversibility vs. Creation of Irreversible Entropy Maximum Entropy, Minimum Internal Energy as a Criterion of Equilibrium Byeong-Joo Lee http: //cmse. postech. ac. kr
Statistical Thermodynamics 의 개본 개념 이해 Ideal Gas에 대한 Statistical Thermodynamics의 응용 력 통계열역학 개념을 통한 엔트로피의 이해 Heat capacity 계산에의 응용 Heat capacity at low temperature Byeong-Joo Lee http: //cmse. postech. ac. kr
Criterion of Thermodynamic Equilibrium, Thermodynamic Relations Helmholtz Free Energy, Gibbs Free Energy의 탄생 배경 Free energy minimum과 equilibrium 간의 상관관계 Chemical Potential의 정의, Gibbs energy와의 관계 Chemical Work으로서의 term Thermodynamic Relation 들의 응용력, 중요성 이해 Byeong-Joo Lee http: //cmse. postech. ac. kr
Numerical Example • A quantity of supercooled liquid Tin is adiabatically contained at 495 K. Calculate the fraction of the Tin which spontaneously freezes. Given J at Tm = 505 K 495 K 1 mole of liquid x moles of solid (1 -x) moles of liquid Byeong-Joo Lee http: //cmse. postech. ac. kr
Example - Phase Transformation of Graphite to Diamond • Calculate graphite→diamond transformation pressure at 298 K, given H 298, gra – H 298, dia = -1900 J S 298, gra = 5. 74 J/K S 298, dia = 2. 37 J/K density of graphite at 298 K = 2. 22 g/cm 3 density of diamond at 298 K = 3. 515 g/cm 3 Byeong-Joo Lee http: //cmse. postech. ac. kr
Gibbs Energy for a Unary System • V(T, P) based on expansivity and compressibility • Cp(T) • S 298: by integrating Cp/T from 0 to 298 K and using 3 rd law of thermodynamics (the entropy of any homogeneous substance in complete internal equilibrium may be taken as zero at 0 K) • H 298: from first principles calculations, but generally unknown ※ H 298 becomes a reference value for GT ※ Introduction of Standard State Byeong-Joo Lee http: //cmse. postech. ac. kr
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