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Unformatted text preview: Lecture note for general thermodynamics, 2003 Summary of thermodynamics CHAPTERS 11-3 •Thermodynamics : •describes macroscopic properties of equilibrium systems •Entirely empirical •Built on 4 laws and simple mathematics •O th law – defines temperature (T) •1 th law – defines energy (U) •2 nd law – Defines entropy (S) •3 rd law – Gives numerical value to entropy •These laws are UNIVERSALLY VALID, they can not be circumvented •Thermodynamic system – control volume which for a fixed mass is a control mass •Definitions •System: the part of the Universe that we choose to study •Surroundings: the rest of the Universe •Boundary: the surface dividing the system from the surroundings •Systems can be: •Open: mass and energy can transfer between the system and the surroundings surroundings •Closed: energy can transfer between the system and the surroundings, surroundings, but NOT mass •Isolated: Neither mass nor energy can transfer between the system system and the surroundings •Describing systems requires: •A few macroscopic properties: p, T, V, n, m,… m,…. •Knowledge if system is homogeneous or heterogeneous •Knowledge if system is in equilibrium state •Knowledge of the number of components •Two classes of properties •Extensive: depends on the size of the system (n, m, V… V…. •Intensive: independent of the size of the system (T,P… (T,P….) •Pure substance: homogeneous + invariable components •Phases: solid, liquid, and vapor (phase diagram) •Phase equilibrium – vaporization, condensation, sublimation, solidification, melting, melting, and the opposite solidifying •P-v-T surface •Saturated liquid/vapor, subcooled liquid(compressed liquid), superheated vapor, and quality (the ratio of the vapor mass to the total mass) •Tables of thermodynamic properties – how to read and use these tables •For real substances – compressibility factor Z used School of Mechanical Engineering, ChungAng University Title Lecture note for general thermodynamics, 2003 •CHAPTERS 44-6 (defines work and heat, and establishes 1st law) •Energy conversion: 1 th law – defines energy (U) •Work and heat: energy transfers between a c.v. and its surroundings surroundings •Work: transferred energy mechanically (or electrically, or chemically) chemically) from one system to another and it must cross the control surface either as a transient phenomenon phenomenon or as a steady state of work, which is power •Displacement work in QuasiQuasi-equilibrium 2 2 1 1 W = mw = ∫ Fdx = ∫ pdV •Polytropic process PVn = constant •Several processes •Quasiequilibrium •Isothermal/Isobaric/Isochoric/Isentropic(rev+adia Isothermal/Isobaric/Isochoric/Isentropic(rev+adia)) •Units •Time(s), Time(s), length(m), length(m), mass(kg), mass(kg), mole(mol, mole(mol, kmol), kmol), force(N) force(N) •Pressure(Pa=1N/m Pressure(Pa=1N/m2, 1bar = 0.1MPa, 1atm=101325Pa) •Temperature (K=273.15+C), specific volume(m3/kg, 1/density) •Work, heat, and energy(J) energy(J) •Simple compressible pure substance: can be defined by two independent independent properties •Work and heat: •both transient/boundary phenomena, path function •Inexact differentials •Sign convention •positive heat (transferred to a system) •positive work (done by a system) •1st law of thermodynamics •During any cycle a system undergoes, the cyclic integral of the heat is proportional to the cyclic integral of the work •Definition of the energy: •exact differential (point function) •properties (U: constant vol., H: constant pressure) dE = dU + d(KE) d(KE) + d(PE) d(PE) = δQ - δW U =U =Uliq + Uvap u = uf + xufg = (1(1-x)uf + xug H = U + PV School of Mechanical Engineering, ChungAng University Title Lecture note for general thermodynamics, 2003 •Specific heats ⎛ ∂h ⎞ ⎛ ∂u ⎞ , Cv = ⎜ CP = ⎜ ⎟ ⎟ ⎝ ∂T ⎠ p ⎝ ∂T ⎠ v Pv = RT R = C p0 − Cv 0 •Control volume dmcv  i − ∑ m e = ∑m dt 1 1 dEcv  i ( hi + Vi 2 + Z i ) − ∑ m  e ( he + Ve2 + Z e ) = Q cv − W cv + ∑ m 2 2 dt •Joule Thomson expansion (coefficient): constant process ⎛ ∂H ⎞ dH = C p dT + ⎜ ⎟ dP = 0 ⎝ ∂T ⎠ T ⎛ ∂H ⎞ ⎛ ∂H ⎞ ⎛ ∂T ⎞ C p dT = − ⎜ dPH , ⎜ = −C p ⎜ ⎟ ⎟ ⎟ ⎝ ∂T ⎠ T ⎝ ∂T ⎠T ⎝ ∂P ⎠ H ⎛ ∂T ⎞ ⎛ ∆T ⎞ µ JT ≡ ⎜ ⎟ = lim ⎜ ⎟ ⎝ ∂P ⎠ H ⎝ ∆P ⎠ H We can measure this Joule-Thomson coefficient •Processes •Steady State: Nozzle, Turbine, Diffuser, Throttle, Pump etc. •Transient: Tank problem •1st law simply describes the energy conservation (equivalence of work work and heat) and the conversion rule. There is no information about the direction of heat and work flows. CHAPTERS 77-9(2nd Law of Thermodynamics, Entropy, •Second law •Puts restrictions on useful conversion of q to w •Follows from observation of a directionality to natural or spontaneous processes •Provides a set of principles for - determining the direction of spontaneous change - determining equilibrium state of system School of Mechanical Engineering, ChungAng University Title Lecture note for general thermodynamics, 2003 •Different statements of the second law •KelvinKelvin-Planck: it is impossible for any system to operate in a cycle that that takes heat from a hot reservoir and converts it to work in the surroundings without at the same time transferring some heat to a colder reservoir T1(hot) T1(hot) q>0 q>0 -w -w q<0 IMPOSSIBLE T2(cold) •Clausius: Clausius: it is impossible for any system to operate in a cycle that takes takes heat from a cold reservoir and transfers it to a hot reservoir without at the same same time converting same work into heat T1(hot) q<0 IMPOSSIBLE -w OK q>0 T2(cold) •Alternative Clausius statement: all spontaneous processes are irreversible (e.g. heat flows from hot to cold spontaneously and irreversibly) irreversibly) •Mathematical statement: defines ENTROPY (state function – point fn.) ⎛δQ ⎞ ∫ dS = ∫1 ⎜⎝ T ⎟⎠ rev 2 •Reversible process (e.g. heat pumps – refrigerators ) •Carnot cycle: operates between the given highhigh-temperature and lowlow-temperature reservoirs and in which every process is reversible •Definitions of thermal efficiency and coefficient of performance (COP) •In Carnot cycle: thermal efficiency is defined as only temperatures of both both reservoirs •Two important thermodynamic relations Tds = du + pdv Tds = dh – vdp •Entropy change of a solid or liquid: ds = du/T du/T = CdT/T CdT/T School of Mechanical Engineering, ChungAng University Lecture note for general thermodynamics, 2003 •Entropy change of an ideal gas 2 S 2 − S1 = ∫ C v o 1 2 S 2 − S1 = ∫ C p o 1 dT v + R ln 2 T v1 dT p − R ln 2 T p1 ∆S > 0 Spontaneous, irreversible ∆S = 0 reversible ∆S < 0 impossible •2nd law of thermodynamics for a control volume ⎛ Q ⎞ dScv  e se = ∑ ⎜ cv ⎟ + S gen − ∑ m i si + ∑ m dt CV ⎝ T ⎠ •Principle of the increase of entropy •says the entropy of an isolated system NEVER decreases •consistent with Clausius inequality •Entropy is a measure of the disorder of a system (isolated) •THIRD LAW : as T->OK, entropy change approaches to zero for all isothermal processes in condensed phases School of Mechanical Engineering, ChungAng University ...
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