Byeong-Joo Lee Byeong-Joo Lee POSTECH - MSE The First Law

Byeong-Joo Lee First Law of thermodynamics - Various Forms of Work 0. Hydrostatic system PdV 1. Surface film SdA 2. Stretched wireFdL 3. Reversible cell εdZ 4. Dielectric slab EdΠ 5. Paramagnetic rod μ o HdM

Byeong-Joo Lee 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

Byeong-Joo Lee 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: U B – U A = -w  Generally: U B – U A = q - w dU = δq - δw : as a state function

Byeong-Joo Lee First Law of thermodynamics - S First Law of thermodynamics - Special processes Absolute value of U is not known: Necessity of Special Paths 1. Constant-Volume Process: ΔU ＝ q v 2. Constant-Pressure Process: ΔH ＝ q p ⇒ 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

Byeong-Joo Lee First Law of thermodynamics - Some issues or dH = C p dT or dU = C v dT or

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

Byeong-Joo Lee First Law of thermodynamics - Numerical Example

Byeong-Joo Lee Byeong-Joo Lee POSTECH - MSE The Second Law

Byeong-Joo Lee 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

Byeong-Joo Lee Second Law of thermodynamics - Reversible vs. Irreversible △ S = measurable quantity + un-measurable quantity = q/T + △ S irr = q rev /T

Byeong-Joo Lee 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

Byeong-Joo Lee Second Law of thermodynamics - Engines and Referigerators

Byeong-Joo Lee ▷ Carnot, 열기관의 효율은 이를 구성하는 두 온도만의 함수. (caloric 이론에 의거 ) ▷ Joule, 에너지는 보존되고, 여러 형태가 서로 변환이 가능함을 실험적으로 제시 → Mayer, Helmholtz 등의 에너지보존법칙에 final touch. ▷ Thomson - Carnot 와 Joule 사이에 모순이 있음을 지적 ▷ Clausius, Joule 을 인정하면서 Carnot 의 원리 증명. 같은 일을 하면서 더 적은 열을 흡수 (q 2 ’) 하고 방출 (q 1 ’) 하는 엔진과 정상적인 Heat Pump 를 결합, q 2 - q 2 ’ = q 1 – q 1 ’. 열이 낮은 온도에서 높은 온도로 흐르지 않는다. 따라서 Carnot 의 원리는 성립한다. ▷ Thomson, Carnot 의 원리 증명 열을 흡수해서 모두 일로 바꾸는 것이 불가능 같은 열을 흡수하면서 더 많은 일과 (w’) 더 적은 열을 방출 (q 1 ’) 하는 엔진과 정상적인 Heat Pump 를 결합, w’- w = q 1 – q 1 ’ 열을 100% 일로 바꿀 수는 없다. 따라서, Carnot 의 원리는 성립한다. ▷ Thomson, 현재 물질 세계에는 역학적 에너지의 낭비를 향한 일반적 경향이 존재한다. ▷ Clausius, 우주의 에너지는 일정하다. 우주의 엔트로피는 항상 증가한다. Second Law of thermodynamics - Historical Background

Byeong-Joo Lee Second Law of thermodynamics - Thermodynamic Temperature Scale → 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 Concept of Absolute Temperature ▷ The maximum efficiency is independent of the working substance and is a function only of the working temperatures, t 1 and t 2.

Byeong-Joo Lee Second Law of thermodynamics - Equivalence of temperature scales Equivalence of Kelvin Scale and Ideal Gas Temperature Scale ▷ Efficiency of Carnot Cycle: ▷ Carnot cycle 이 두 개의 reversible isothermal process 와 두 개의 reversible adiabatic process 로 이루어졌다고 가정하고 ideal gas temperature scale 에 기초하여 효율을 계산하면 (T 2 -T 1 )/T 2 라는 같은 결과나 나온다.

Byeong-Joo Lee Second Law of thermodynamics - Entropy as a State Function ※ 로 정의되는 entropy S 는 state function 이고 adiabatic system 에서 감소할 수 없다. For a Carnot Cycle For an arbitrary Cyclic process which can be broken into a large number of small Carnot cycle.

Byeong-Joo Lee 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)

Byeong-Joo Lee Second Law of thermodynamics - Maximum Work

Byeong-Joo Lee 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.

Byeong-Joo Lee 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.

Byeong-Joo Lee Second Law of thermodynamics – Numerical Example