이 병 주 포항공과대학교 신소재공학과 calphad@postech.ac.kr

1. 이 병 주 포항공과대학교 신소재공학과 calphad@postech.ac.kr Thermodynamics The First Law

2. First Law of thermodynamics - Various Forms of Work 0. Hydrostatic system PdV 1. Surface film SdA 2. Stretched wire FdL 3. Reversible cell εdZ 4. Dielectric slab EdΠ 5. Paramagnetic rod μoHdM

3. First Law of thermodynamics - Is Heat an Energy? ▷ Count Rumford (1798): heat produced during boring of cannon was roughly (Benjamin Thompson) proportional to the work performed during the boring ▷ Humphrey Davy (1799): End of Caloric Theory ← Melting of two blocks of ice by rubbing them in vacuum ▷ Mayer, Helmholtz 등 에너지 보존 법칙의 가능성을 언급 ▷ James Joule observed: (1840 ∼) A direct proportionality existed between the work done and the resultant temperature rise. The same proportionality existed no matter what means were employed in the work production · Rotating a paddle wheel immersed in the water · A current through a coil immersed in the water · Compressing a cylinder of gas immersed in the water · Rubbing together two metal blocks immersed in the water ※ Mechanical equivalent of heat with unit calorie

4. First Law of thermodynamics - First Law • “The change of a body inside an adiabatic enclosure from a • given initial state to a given final state involves the same • amount of work by whatever means the process is carried • out” • It was necessary to define some function which depends only on the internal state of a body or system – Internal Energy. • For adiabatic process: UB – UA = -w • Generally: UB – UA = q - w • dU = δq - δw • : as a state function

5. First Law of thermodynamics - Special processes Absolute value of U is not known: Necessity of Special Paths 1.Constant-Volume Process: ΔU ＝ qv 2. Constant-Pressure Process: ΔH ＝ qp ⇒ concept of heat capacity: , , 3. Reversible Adiabatic Process: q ＝ 0 4. Reversible Isothermal Process: ΔU ＝ ΔH ＝ 0 ※ Importance of the identification of state functions → justification of the analysis of unrealistic reversible processes

6. First Law of thermodynamics - Some issues or dU = Cv dT or dH = Cp dT or or

7. First Law of thermodynamics - Special Processes Reversible Adiabatic Process: q ＝ 0 for ideal gas = constant Reversible Isothermal Process: ΔU ＝ ΔH ＝ 0

8. First Law of thermodynamics - Numerical Example

9. 이 병 주 포항공과대학교 신소재공학과 calphad@postech.ac.kr Thermodynamics The Second Law

10. Second Law of thermodynamics - Introduction Spontaneous (or Natural or Irreversible) Process ▷ mixing of two gases ▷ Equalization of temperature ▷ A + B = C + D : criterion for equilibrium? Entropy as a measure of the degree of irreversibility ▷ Lewis and Randall’s Consideration: A weight-pulley-heat_reservoir ▷ q/T = △S

11. Second Law of thermodynamics - Reversible vs. Irreversible △S = measurable quantity + un-measurable quantity = q/T + △Sirr = qrev/T

12. Second Law of thermodynamics - Evaluation of Entropy Change ▷ Reversible Isothermal Compression of an Ideal Gas ▷ Reversible Adiabatic Expansion of an Ideal Gas Isentropic process: ΔU = -w

13. Second Law of thermodynamics - Engines and Referigerators

14. ▷ Carnot, 1824 - 열기관의 효율은 이를 구성하는 두 온도만의 함수. (caloric 이론에 의거) ▷ Joule, 1847 - 에너지는 보존되고, 여러 형태가 서로 변환이 가능함을 실험적으로 제시 → Mayer, Helmholtz 등의 에너지보존법칙에 final touch. ▷ Thomson - Carnot와 Joule 사이에 모순이 있음을 지적 ▷ Clausius, 1850 - Joule을 인정하면서 Carnot의 원리 증명. 같은 일을 하면서 더 적은 열을 흡수(q2’)하고 방출(q1’)하는 엔진과 정상적인 Heat Pump를 결합, q2 - q2’ = q1 – q1’. 열이 낮은 온도에서 높은 온도로 흐르지 않는다. 따라서 Carnot의 원리는 성립한다. ▷ Thomson, 1851 - Carnot의 원리 증명 열을 흡수해서 모두 일로 바꾸는 것이 불가능 같은 열을 흡수하면서 더 많은 일과(w’) 더 적은 열을 방출(q1’)하는 엔진과 정상적인 Heat Pump를 결합, w’- w = q1 – q1’ 열을 100% 일로 바꿀 수는 없다. 따라서, Carnot의 원리는 성립한다. ▷ Thomson, 1852 - 현재 물질 세계에는 역학적 에너지의 낭비를 향한 일반적 경향이 존재한다. ▷ Clausius, 1865 - 우주의 에너지는 일정하다. 우주의 엔트로피는 항상 증가한다. Second Law of thermodynamics - Historical Background

15. Second Law of thermodynamics - Thermodynamic Temperature Scale • Concept of Absolute Temperature • ▷ The maximum efficiency is independent of the working substance • and is a function only of the working temperatures, t1 and t2. Kelvin Scale (Absolute Thermodynamic Temperature Scale, K) → 0K is the temperature of the cold reservoir which makes the efficiency Of a Carnot cycle equal to unity

16. Second Law of thermodynamics - Equivalence of temperature scales Equivalence of Kelvin Scale and Ideal Gas Temperature Scale ▷Efficiency of Carnot Cycle: ▷ Carnot cycle이 두 개의 reversible isothermal process와 두 개의 reversible adiabatic process로 이루어졌다고 가정하고 ideal gas temperature scale에 기초하여 효율을 계산하면 (T2-T1)/T2라는 같은 결과나 나온다.

17. Second Law of thermodynamics - Entropy as a State Function For a Carnot Cycle For an arbitrary Cyclic process which can be broken into a large number of small Carnot cycle. ※로 정의되는 entropy S는 state function이고 adiabatic system에서 감소할 수 없다.

18. Second Law of thermodynamics - Entropy and Irreversibility ▷ Processes exhibiting Mechanical Irreversibility Coming to rest of a rotating or vibrating liquid in contact with a reservoir Ideal gas rushing into a vacuum ▷ Processes exhibiting Thermal Irreversibility Conduction or radiation of heat from hotter to cooler system/reservoir ▷ Processes exhibiting Chemical Irreversibility Mixing of two dissimilar inert ideal gases (※ example: k ln Ω, ln x! = x ln x – x ) Freezing of supercooled liquid (※ example: freezing of supercooled Pb)

19. Second Law of thermodynamics - Maximum Work

20. Second Law of thermodynamics - Entropy as a Criterion of Equilibrium ※ for an isolated system of constant U and constant V, (adiabatically contained system of constant volume) equilibrium is attained when the entropy of the system is maximum. ※ for a closed system which does no work other than work of volume expansion, dU = T dS – P dV (valid for reversible process) U is thus the natural choice of dependent variable for S and V as the independent variables. ※ for a system of constant entropy and volume, equilibrium is attained when the internal energy is minimized.

21. Second Law of thermodynamics - Condition for Thermodynamic Equilibrium ※ Further development of Classical Thermodynamics results from the fact that S and V are an inconvenient pair of independent variables. + need to include composition variables in any equation of state and in any criterion of equilibrium + need to deal with non P-V work (e.g., electric work performed by a galvanic cell) ※ Condition for Thermodynamic Equilibrium of a Unary two phase system The same conclusion is obtained using minimum internal energy criterion.

22. Second Law of thermodynamics – Numerical Example