Thermodynamics The First Law ByeongJoo Lee POSTECH MSE

Thermodynamics The First Law Byeong-Joo Lee POSTECH - MSE calphad@postech. ac. kr Byeong-Joo Lee http: //cmse. postech. ac. kr

First Law of thermodynamics - Various Forms of Work 0. Hydrostatic system Pd. V 1. Surface film Sd. A 2. Stretched wire Fd. L 3. Reversible cell εd. Z 4. Dielectric slab EdΠ 5. Paramagnetic rod μo. Hd. M Byeong-Joo Lee http: //cmse. postech. ac. kr

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 http: //cmse. postech. ac. kr

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 d. U = δq - δw : as a state function Byeong-Joo Lee http: //cmse. postech. ac. kr

First Law of thermodynamics - Special processes S 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 Byeong-Joo Lee http: //cmse. postech. ac. kr

First Law of thermodynamics - Some issues or d. U = Cv d. T or d. H = Cp d. T or or Byeong-Joo Lee http: //cmse. postech. ac. kr

First Law of thermodynamics - Special Processes Reversible Adiabatic Process: q ＝ 0 for ideal gas = constant Reversible Isothermal Process: ΔU ＝ ΔH ＝ 0 Byeong-Joo Lee http: //cmse. postech. ac. kr

First Law of thermodynamics - Numerical Example Byeong-Joo Lee http: //cmse. postech. ac. kr

Thermodynamics The Second Law Byeong-Joo Lee POSTECH - MSE calphad@postech. ac. kr Byeong-Joo Lee http: //cmse. postech. ac. kr

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 http: //cmse. postech. ac. kr

Second Law of thermodynamics - Reversible vs. Irreversible △S = measurable quantity + un-measurable quantity = q/T + △Sirr = qrev/T Byeong-Joo Lee http: //cmse. postech. ac. kr

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 http: //cmse. postech. ac. kr

Second Law of thermodynamics - Engines and Referigerators Byeong-Joo Lee http: //cmse. postech. ac. kr

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, t 1 and t 2. Kelvin Scale (Absolute Thermodynamic Temperature Scale, K) → 0 K is the temperature of the cold reservoir which makes the efficiency Of a Carnot cycle equal to unity Byeong-Joo Lee http: //cmse. postech. ac. kr

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 (T 2 -T 1)/T 2라는 같은 결과나 나온다. Byeong-Joo Lee http: //cmse. postech. ac. kr

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. Byeong-Joo Lee http: //cmse. postech. ac. kr

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 http: //cmse. postech. ac. kr

Second Law of thermodynamics - Maximum Work Byeong-Joo Lee http: //cmse. postech. ac. kr

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, d. U = T d. S – P d. V (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 http: //cmse. postech. ac. kr

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 http: //cmse. postech. ac. kr

Second Law of thermodynamics – Numerical Example Byeong-Joo Lee http: //cmse. postech. ac. kr