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 wPV=−−Fh = VExpansion0 :; VCompression 0:
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 )VP=1or Vconst(n,T ) Robert Boyle 1627-1691 Amontons' (Gay− Lussac' s) Law P(T ) =+P(01)T C T
0 Charles' Law V(TCC )=+→ V(C)TV(T)T01 (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 PkT= B 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.
PVnRTNkT== B
Force F = P·A→ P·V = energy content
Idealization: At T=0 : P = 0, V = 0. Idealization not viable at T=0 high high matter density→ particles interact
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 dqdSdU=00,0 →== Calculation for1 mole ideal gas 0 ==+dq →= dU − p dVdUp dV U U dU( V, Td) = V +=dT CV dT V T T V RT 0 =+C =+ dT p dV C dTdV 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