NPRENPRE--470470 FuelFuel CellCell ThermodynamicsThermodynamics Chapter 2 of Fuel Cell Fundamentals Chapter 2 and Appendix-A Dr. Kyu-Jung Kim of Fuel Cell Systems Explained Department of Nuclear, Plasma and Radiology Engineering University of Illinois

1 TopicsTopics

. What is Thermodynamics ?

. Gibbs Free Energy

. Gibbs Free Energy & Voltage

. Reversible Voltage & Temperature

. Reversible Voltage & Pressure

. Reversible Voltage & Concentration

. Fuel Cell Efficiency

. Thermal & Mass Balance in Fuel Cell

2 WhatWhat isis ThermodynamicsThermodynamics ??

““ItIt isis importantimportant toto realizerealize thatthat inin modernmodern physicsphysics today,today, wewe havehave nono knowledgeknowledge ofof whatwhat energyenergy is.is.”” Richard Feynman Lectures on Physics

3 WhatWhat isis ThermodynamicsThermodynamics ??

• Zeroth law of thermodynamics: If two systems are in thermal equilibrium with a third system, they must be in thermal equilibrium with each other. This law helps define the notion of temperature.

• First law of thermodynamics: Heat and work are forms of energy transfer.

• Second law of thermodynamics: The entropy of any closed system not in thermal equilibrium almost always increases.

• Third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches zero.

4 WhatWhat isis ThermodynamicsThermodynamics ??

The 1st Law of Thermodynamics says; Energy can be transferred from one system to another in many forms. However, it can not be created nor destroyed. Thus, the total amount of energy available in the Universe is constant. E = MC2 Energy (E) is equal to matter (M) times the square of a constant (C). Einstein suggested that energy and matter are interchangeable. His equation also suggests that the quantity of energy and matter in the Universe is fixed.

Matter is the material (atoms and molecules) that constructs things on the Earth and in the Universe.

System is a set of interrelated components working together towards some kind of process.

Energy is defined as the capacity for doing work. Energy can exist the following forms: radiation; kinetic energy; potential energy; chemical energy; atomic energy; electromagnetic energy; electrical energy; and heat energy.

5 WhatWhat isis ThermodynamicsThermodynamics ??

The 2nd Law of Thermodynamics says; Natural processes that involve energy transfer must have one direction, and all natural processes are irreversible. It also predicts that The entropy of an isolated system always increases with time. As a result of this fact both energy and matter in the Universe are becoming less useful as time goes on.

COSMOSCOSMOS Irreversible CHAOSCHAOS Order process Order DisorderDisorder

ENERGYENERGY ReleaseRelease

Entropy is the measure of the disorder or randomness of energy and matter in a system. 6 WhatWhat isis ThermodynamicsThermodynamics ?? The 2nd Law of Thermodynamics in the ancient literature; The Bible

Genesis 1:1 ENDEAVORENDEAVOR PlanPlan & & Work Work

CHAOSCHAOS COSMOSCOSMOS Order DisorderDisorder Order

In the beginning God created the heaven and the earth.

7 FourFour ThermodynamicThermodynamic PotentialsPotentials --TSTS

Internal Helmholtz UU Energy FF Free Energy F = U - TS U = energy needed to F = energy needed to create create a system a system minus the energy ++pVpV provided by the environment Enthalpy Gibbs HH GG Free Energy H = U + pV G = U + pV - TS

H = energy needed to create G = total energy to create a a system plus the work system and make room for it needed to make room for it minus the energy provided by the environment

8 GibbsGibbs FreeFree EnergyEnergy

““EnergyEnergy availableavailable toto dodo externalexternal work,work, neglectingneglecting anyany workwork donedone byby changeschanges inin pressurepressure and/orand/or volume.volume.””

. Hydrogen Fuel Cell Reaction

1 2  2 2  2OHOH

Hydrogen Electricity, W Δh Energy Reactants Fuel Cell Heat, Q released Oxygen Water Products

W=ΔGf = Gf of products -Gf of reactants = Maximum available thermodynamic work potential

9 GibbsGibbs FreeFree EnergyEnergy

Hydrogen Electricity, W Δh Energy Reactants Fuel Cell Heat, Q released Oxygen Water Products

W=ΔGf = Gf of products -Gf of reactants = Maximum available thermodynamic work potential

g f  0 g f  0 g f  0 Spontaneous Equilibrium Non-spontaneous

10 GibbsGibbs FreeFree EnergyEnergy

““ChangeChange inin MolarMolar GibbsGibbs FreeFree Energy.Energy.””

. Gibbs Free Energy of a System

 TSHG

. Molar Gibbs Free Energy of Formation

ff  sThg

. Changes in Molar Gibbs Free Energy of Formation

ff  sThg

11 GibbsGibbs FreeFree EnergyEnergy

. Changes in Molar Gibbs Free Energy of Formation

ff  sThg

. Changes in Molar Entropy     1 ssss )()()( 2OH H 2 2 O2

. Changes in Molar Enthalpy of Formation

 1 hhhh )()()( 2 HfOHff 2 2 Of 2

Products Reactants

12 GibbsGibbs FreeFree EnergyEnergy

. Δhf and Δs at temperature T when cp as Molar Heat Capacity at constant pressure T T  dTchh  1 dTcss  PoT oT  T P To To

o . ho and so = Molar Enthalpy of Formation and Entropy at 298.15 K (25 C)

ho (kJ/mol) so (kJ/molK)

H2O (liquid) -285.84 69.95

H2O (steam) -241.83 188.83

H2 0 130.59

O2 0 205.14

13 GibbsGibbs FreeFree EnergyEnergy

. Molar Heat Capacity at constant pressure for Steam

c  T 25.0  T 5.0  036989.02751.8040.5805.143 T P 2OH )(

Cp (H2O)

35.00

34.80

34.60

34.40

34.20 Cp (J/mol K)

34.00 cp (H2O) 33.80

33.60

290 340 390 440 490 Temp (K) Thermodynamics, Gordon Van Wylen, 1989 14 GibbsGibbs FreeFree EnergyEnergy

. Molar Heat Capacity at constant pressure for Hydrogen

c  6.22222505.56 T  75.0 116500T 1  560700T  5.1 HP 2 )(

Cp (H2)

29.4

29.2

29.0

28.8

28.6 Cp (J/mol K) 28.4 cp (H2)

28.2

28.0 290 340 390 440 490 Temp (K) Thermodynamics, Gordon Van Wylen, 1989 15 GibbsGibbs FreeFree EnergyEnergy

. Molar Heat Capacity at constant pressure for Oxygen

c 100102.2432.37  T 5.15  178570T  5.1  2368800T 2 OP 2 )(

Cp (O2)

31.00

30.80

30.60

30.40

30.20

Cp (J/mol K) 30.00

29.80 cp (O2) 29.60

29.40

290 340 390 440 490 Temp (K) Thermodynamics, Gordon Van Wylen, 1989 16 GibbsGibbs FreeFree EnergyEnergy

. Calculated values of Δhf , Δs and Δgf

ff  sThg

 1 hhh )()()(     1 sssT )()()(  = 2 HfOHf 2 2 Of 2 2OH H 2 2 O2

 T   T  1  T    dTch    dTch    dTch  =  2OHo  2OHP   Ho 2  HP 2  2  Oo 2  OP 2   To   To   To 

 T   T  1  T   1   1   1   sT OHo  T OHP dTc Ho  T HP dTcs Oo  T OP dTcs   2  2   2  2  2  2  2   To   To   To 

17 GibbsGibbs FreeFree EnergyEnergy

. Calculated values of Δhf , Δs and Δgf

ff  sThg

o Temp C(K) Δhf (kJ/mol) Δs (J/molK) Δgf (kJ/mol) 100 (373.15) -242.6 -46.6 -225.2 300 (573.15) -244.5 -50.7 -215.4 500 (773.15) -246.2 -53.3 -205.0 700 (973.15) -247.6 -54.9 -194.2 900 (1173.15) -248.8 -56.1 -183.1

Negative value means that energy is released.

18 GibbsGibbs FreeFree EnergyEnergy . Example 2-2

g )(2   HCOOHCO 22

ff  sThg  hhhhh )()()()( COff 2 2 2OHfCOfHf = (-393.51) + (0) – (-110.53) – (-241.83) = -41.13 kJ/mol     sssss )()()()( CO2 H 2 CO 2OH = (213.80) + (130.67) – (197.65) – (188.82) = -42.00 J/mol·K

g f = - 41.13 + 0.042 T (kJ/mol) * Assume Δh and Δs to be independent of temperature

g f  0 g f  0 g f  0 Spontaneous Equilibrium Non-spontaneous T = 979 K or 706 oC cf) Δg = -55.03 + 0.032 T T = 1720 K when Δh and Δs values at 980 K 19 GibbsGibbs FreeFree EnergyEnergy && VoltageVoltage

. Electrical Work done by a charge Q (Ahr) and potential difference E (V)

elec   EQW

. Charge done by number of moles of electrons n and a charge per one mole of electron F   FnQ Faraday’s constant = (6.022x1023 e-/mol)  (1.68x10-19 C/e-) = 96,400 Coulombs/mol

. Electrical work as a change of Gibbs free energy of formation

elec  f     EFngW

20 GibbsGibbs FreeFree EnergyEnergy && VoltageVoltage

. Hydrogen Fuel Cell Reaction

1 2 2 2  2OHOH

. Reversible Voltage generated by H2 -O2 Fuel Cell under STP

1 go  gg  gg )()()( E  ff 2 lOH )( f H 2 2 f O2 o  Fn -306.69 - ( -38.96 ) - ½ ( -61.12 ) -237,000 J/mol  (2 mol of e- /mol of reactant)  (96,400 Coulombs/mol)

= + 1.23 V

21 ReversibleReversible VoltageVoltage && TemperatureTemperature

. Differential Expression of Gibbs Free Energy

 TSpVUG

     SdTTdSVdppdVdUdG

  pdVTdSdU

  dWdQdU dW )( mech  pdV 1st law of thermodynamics dQ dS  T   SdTVdpdG  TdSdQ

2nd law of thermodynamics 22 ReversibleReversible VoltageVoltage && TemperatureTemperature

. Differential Expression of Gibbs Free Energy   SdTVdpdG  dG   gd )(     S    s  dT  p Molar reaction  dT  p quantities

. Gibbs Free Energy & Reversible Voltage

    EFng

 dE  s s    EE oT  TT o )(  dT  p  Fn  Fn

23 ReversibleReversible VoltageVoltage && TemperatureTemperature

. Example : Reversible Voltage at 1000 K

    1 ssss )()()( 2 gOH )( H 2 2 O2

= 188.84 – 130.68 – ½ (188.82) s = -44.34 J/mol·K @ STP* EE  TT )( oT  Fn o * Assume Δs to be independent of temperature

-44.34 J/mol·K x (1000 K – 298.15 K) = 1.23 + (2 mol of e- /mol of reactant)  (96,400 Coulombs/mol)

= 1.069 V

Actual Δs at 1000 K is 55.3 J/mol·K  ET = 1.15 V 24 ReversibleReversible VoltageVoltage && PressurePressure

. Differential Expression of Gibbs Free Energy   SdTVdpdG  dG   gd )(     V    v    dp   dp T Molar reaction   p quantities

. Gibbs Free Energy & Reversible Voltage

    EFng nproducts - nReactants

 dE  v  dE   g RTn        dp T  Fn  dp T  pFn

25 ReversibleReversible VoltageVoltage && ConcentrationConcentration

. Chemical potential related concentration through Activity p   o   ln aTR a  po Reference chemical potential at STP Partial pressure, p at STP = 1atm . Chemical potential of an arbitrary reaction

   nNmMbBaA m n M aa N Mo No Ao Bo TRbanmg  ln a b A aa B m n M aa N o TRg  ln a b A aa B van’t Hoff isotherm 26 ReversibleReversible VoltageVoltage && ConcentrationConcentration

. Voltage as a function of Chemical Activity

m n M aa N o TRgg  ln a b A aa B      EFng

m n TR M aa N EE o  ln a b  Fn A aa B Nernst Equation    nNmMbBaA

27 ReversibleReversible VoltageVoltage && ConcentrationConcentration

1 . Example of H2 ~O2 Fuel Cell   OHOH 2 2 2 2 Liquid water under 100 oC a TR 2OH TR 1 EE o  ln 1 Eo  ln 1 2 F aa 2 2 F  pp 2 OH 22 2 OH 2

if the fuel cell is under operation on H2 at 3 atm and air at 5 atm

  15.298314.8  1 E 229.1  ln 1 964002  21.053 2

Partial pressure of O at 5 atm = 1.244 V 2

28 Pressure,Pressure, TemperatureTemperature andand NernstNernst EquationEquation

. Nernst Equation for T ≠ To

m n TR M aa N EE T  ln a b  Fn A aa B s EE  TT oT  Fn o

m n s TR M aa N EE o  TT o  ln a b  Fn  Fn A aa B Nernst Equation    nNmMbBaA

29 ConcentrationConcentration CellsCells

. As an implication of Nernst Equation

m n 8 TR M aa N  15.298314.8  10 EE o  ln a b 0  ln  Fn A aa B 964002 100 = 0.296 V

30 FuelFuel CellCell EfficiencyEfficiency Thermodynamic

useful energy work    1 total energy hHHV 2  2 2  2OHOH

 gg  1 gg )()()( ff 2 lOH )( f H 2 2 f O2 g  17.237 @ STP  thermoFC    83.0 hHHV  286  0.77 @ 480 K

TT LH  Carnot  TH

31 FuelFuel CellCell EfficiencyEfficiency Thermodynamic

g  FC  h PEMFC PAFC SOFC

TT LH  Carnot  TH

32 FuelFuel CellCell EfficiencyEfficiency Practical

  acticalprFC   thermoFC  voltageFC   utilfuelFC

i Current generation (A/cm2) Vop  Fn E v Molar rate of rev fuel actual fuel feed (mol/s)

 g   Vop   1       v fuel  acticalprFC         1  hHHV   Erev     i  Fn = Stoichiometric Ratio

33 FuelFuel CellCell EfficiencyEfficiency Practical

v   fuel i  Fn

10% more than needs

34 ThermalThermal && MassMass BalanceBalance inin FuelFuel CellCell Q i  heat   PPP elecin s   vFn  iVvh

   h  where J/s J/mol mol/s cons v     iV   cons   Fn  cons i in  vhP   n  F     iVE  heat  PP elec Hcons      iViE  heat  iVP Hcons Pin Pelec

h Imaginary voltage without physical meaning E  h Molar enthalpy of reactant fuel H  Fn vcons Molar consumption rate of reactant fuel 35 ThermalThermal && MassMass BalanceBalance inin FuelFuel CellCell

h EH   Fn E g O  0.17 EH h gO EO   Fn = 0.83

of H2 -O2 fuel cell = Total energy loss in a Fuel Cell = Heat

Pheat  cons  H  iVE 0.83

36 ThermalThermal && MassMass BalanceBalance inin FuelFuel CellCell

. Fuel input rate vs. Product output rate

Example : H2~Air FC of 1000 kA generation with 20 mol/s of air feeding rate i Hydrogen Electricity (1 kA) Air (20 mol/s) Fuel Cell Heat vv inout   0  Fn Air out Water i i vv  wv   2 OinOout 2  Fn  OAirin 2  Fn 1000kA  smol 21.0/20   /6.1 smol  /964004 molC

i kA)(1000 vv    smol )/(19.5 2 HOH 2  Fn  molC )/(964002

37 ThankThank youyou

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