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Thermodynamics: Phenomenology • Work and other forms of energy Reading Assignments Weeks 11&12 Transfer and dissipation LN V-VI: • 1. & 2. Fundamental Laws of Thermodynamics • Ideal-gas laws and simple processes Kondepudi Ch. 3 & 4 Additional Material Technological applications, cyclic engines • Real gases equation of state McQuarrie & Simon Ch. 5 & 6 Technological applications • Phase equilibria • Free energy in chemical reactions • Thermochemistry, electrochemistry • Kinetic theory of gases W. Udo Schröder 2021 Phenomen 1&2. LTD 1 Ideal-Gas Laws: Simple Processes Compression of a gas volume, at pressure equilibrium, P = Pext = atmospheric pressure h PFAP==/ ext w=−Fh = − P V V0 : Expansion ; V 0: Compression Sign Convention: Work is counted positive (w > 0) when it increases the internal energy U of a gas. W. Udo Schröder 2021 Phen_Process 2 Gas Laws: Ideal-Gas Equation of State EoS Robert Boyle, Guillaume Amontons, Gay-Lussac Response of dilute gases of specified amounts (#moles = n, Avogadro) Boyle' s Law P(V )1 V or P V = const(n,T ) Robert Boyle 1627-1691 Amontons' (Gay− Lussac' s) Law P(T ) =P(01)T + C T 0 Charles' Law V(T)CC= V(01 C) + T → V(T) T(Kelvin) ≈ 3.66·10-3/0C ≈ 1/2730C → absolute temperature T Compression Robert Boyle: gas pressure p increases with Guillaume Amontons 1663-1705 external force F = p·A, scales with number of F particles (N) or (n) of gas moles A V p EoS of P V = n R T = N kB T Ideal Gases P= kB T Joseph Louis Gay-Lussac 1778-1850 Dalto n' s L aw partial pressuresP= Pi W. Udo Schröder 2021 Phenomen 1&2. LTD i 3 Amontons' Paper and Setup W. Udo Schröder 2021 Phenomen 1&2. LTD 4 Ideal-Gas Equation of State EoS Complete description of macroscopic equilibrium state of any dilute gas: Ideal gases have only one phase (g) State Functions (variables) Pressure P, volume V, temperature T. Force F = P·A→ P·V = energy content Idealization: At T=0 : P = 0, V = 0. Idealization not viable at T=0 high high matterP V = density n R → Tparticles = N kB interact T Gas Constant R = 8.31451 J/(K·mole) -23 Boltzmann Constant kB = 1.38.10 J/K W. Udo Schröder 2021 Phenomen 1&2. LTD 5 The (Ideal-Gas) Equation of State p·V = n·R·T; n=# moles, T→ U Non-interacting → Only gas phase! A: p(V,T)= n R T/V A Ideal Gas Constant R R = 0.0821 liter·atm/mol·K R = 8.3145 J/mol·K R = 8.2057 m3·atm/mol·K R = 62.3637 L·Torr/mol·K or L·mmHg/mol· State functions p, V, T,… . Molar p(V,T) hyper-plane (monotonic) contains all possible gas states A. There are no other states of the gas. W. Udo Schröder 2021 Phen_Process 6 The Adiabatic Equation of State Relation between internal energy of ideal gas and pressure-volume relation. Adiabatic expansion means (here) no exchange of heat energy, dq = 0. q = 0 dq=0 → dS = 0, dU = 0 Calculation for1 mole ideal gas 0 =dq = dU + p dV → dU = − p dV U U dU( V, T) = dV +dT = CV dT V T T V RT 0 =C dT + p dV = C dT + dV VVV dT dV dTCC− dV PV −1 CRV + =00 → + = T= V const. TVTCVV p= V const. cp dT dV =; +( − 1) = 0 T= p1− const. cV T V W. Udo Schröder 2021 Phenomen 1&2. LTD 7 Pressure Units W. Udo Schröder 2021 Phen_Process 8.

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