FUEL CELL FUNDAMENTALS (Chapter. 2)

Chapter 2. 연료전지 열역학 The purpose of this chapter ◈ 2 장의 목적 √ 열역학 : 한 형태에서 다른 형태로 에너지 변환, 에너지론의 한 분야 √ 연료전지 : 에너지 변환장치 √ 연료전지 열역학 : 화학에너지의 전기적 에너지 변환 이해하는 열쇠 - 연료전지 반응이 자발적인가 판단 - 최대전압 한계 값 제시 - 연료전지에서 가능한 이론적인 이상적인 경우 제시 √ 연료전지 성능 이해 : 열역학, 동역학 지식 필요

2.1. Thermodynamics Review Chapter 2. Fuel Cell Thermodynamics 내부 에너지 What Is Thermodynamics? ◈ 내부 에너지 (U) √ 원자, 분자규모 미소한 운동과 입자들 사이 : 상호작용 관계된 에너지 √ 내부 에너지 ⇒ 화학결합과 관계 √ 내부 에너지 변환 량 ⇒ 열역학 1, 2 법칙 ⇒ Figure 2.1 √ Richard Feynman : 에너지가 무엇인지 우리는 아는 게 없다. ⇒ Law of thermodynamics, enthalpy, free energy How quantity(energy, temperature, pressure, volume) are related

Internal Energy Chapter 2. Fuel Cell Thermodynamics Figure 2.1. Although this tank of H 2 gas has no apparent macroscopic energy, it has significant internal energy. Internal energy is associated with microscopic movement (kinetic energy) and interactions between particles (chemical/ potential energy) on the atomic scale.

열역학 제 1 법칙 √ 에너지 보존법칙 Chapter 2. Fuel Cell Thermodynamics ◈ The first law of thermodynamics (2.1) (2.2) (2.3) (2.4) (2.5)

일 과 열일 과 열 일, 열 : 운반 상태의 에너지, 주변의 환경이 나 사람들의 몸 사이에 전달되는 에너지 일 : 어떤 거리를 이동 힘을 가하면 이러한 에 너지가 전달 열 : 온도 차에 의해 에너지 전달 열역학 제 2 법칙 : 열은 100% 일로 변환될 수 없다 열 병목현상 : 연료전지는 열변환 단계 우회

Second Low Chapter 2. Fuel Cell Thermodynamics √ 엔트로피 : 시스템 가능한 미소상태 수, 시스템을 구성하는 가능한 방법 수 √ 엔트로피 : 무질서도 측정 ☞ 가장 간단한 고립 시스템 ◈ The second law of thermodynamics (2.6) Where,

Second Low Chapter 2. Fuel Cell Thermodynamics Figure 2.2. (a) The entropy of this 100 atom perfect crystal is zero because there is only one possible way to arrange the atoms to produce this configuration (b) When three atoms are removed from the crystal and placed on the surface, the entropy increases. This is because there are many possible always to configure a system of 100 atoms where 3 have been removed.

Second Low Chapter 2. Fuel Cell Thermodynamics √ 총 Z 개의 원자들 중 N 개의 원자를 취하는 경우 시스템 구성이 가능한 미소 상태수 : (2.7) ☞ 그림 2.2b, 100 개의 원자 중 3 개를 취하는 가능한 방법 수 (2.8) ☞ This is yields S=7.22 ⅹ J/K.

Second Low Chapter 2. Fuel Cell Thermodynamics √ 일정한 압력의 가역 열 전달 계에서, 시스템의 엔트로피 변화 : (2.9) (2.10) √ 열역학 제 2 법칙에서 시스템과 그 주위의 계의 엔트로피의 변화는 증가하거나 최소한 0 이 된다 : √ 실제 엔트로피를 정확히 계산할 수 없으나, 열 전달이 시스템 엔트로피를 얼마나 변화시키는지에 근거하여 유추

열역학적 퍼텐셜 Chapter 2. Fuel Cell Thermodynamics ◈ 시스템의 내부 에너지 ☞ 식 (2.3) 과 (2.9) 로부터, TdS ⇒ 가역적인 열 전달, pdV ⇒ 기계적인 일 (2.11) (2.12) (2.13) (2.14)

Thermodynamic Potentials Chapter 2. Fuel Cell Thermodynamics √ S 와 V 의 측정 어려움. T, P 로 측정하여 변환. 새로운 열역학적 퍼텐셜 G(T, P) 정의 : (2.15) ☞ (dU/dS) V = T 와 (dU/dV) S = -p : (Gibbs free energy) (2.16) √ G 의 변화 ( 수학적 dG) : (2.17) ☞ dU = TdS – pdV : (2.18)

Thermodynamic Potentials Chapter 2. Fuel Cell Thermodynamics √ 식 (2.15) 와 유사하게 열역학 퍼텐셜 H : (2.19) ☞ (dU/dV) S = -p: H : 엔탈피 (2.20) (2.21) ☞ dU = TdS – pdV 적용 (2.22) ☞ 미분

Thermodynamic Potentials Chapter 2. Fuel Cell Thermodynamics √ 헬름홀츠 (Helmholtz) 자유 에너지 (F) : (2.23) ☞ 미분, 계산 : (2.24) √ U : 온도, 부피 변화 없는 경우☞ 시스템 구성에 필요한 에너지 H : U+( 부피 0 부터 ) 시스템 차지 공간 만드는데 필요한 일 F : U – 등온상태 열 전달로 시스템 주변으로부터 얻는 에너지

Thermodynamic Potentials Chapter 2. Fuel Cell Thermodynamics Figure 2.3. Pictorial summary of the four thermodynamic potentials. They relate to one another by offsets of the “energy from environment” term TS and the “expansion work” term pV. Use this diagram to help remember the relationships.

Chapter 2. Fuel Cell Thermodynamics √ 몰 양은 고유한 양, 화학반응에서 몰 양 근거 에너지 변화 계산 △ → 열역학 과정에서 초기상태와 최종상태 사이의 변화 표준 상태 √ 실온 : 25 ℃ → K √ 대기압 : 1 bar → 100 kPa, 1atm → kPa ◈ STP (standard temperature and pressure) 몰 용량 ◈ 몰 용량 √ 고유 (Intrinsic) : T, P → 시스템의 크기에 무관 √ 비고유 (Extrinsic) : 내부에너지, 엔트로피 → 시스템 크기와 연관

가역성 ◈ 가역성 Chapter 2. Fuel Cell Thermodynamics √ 가역적 : 열역학적 평형 √ 가역적 연료전지 전압 : 열역학적 평형에서 연료전지에 의해 생성된 전압 √ 가역적인 연료전지 전압 식들은 평형상태 조건에서 적용 - E : 열역학적으로 예상되는 가역적인 전압 - V : 연료전지의 비가역적인 작동전압

◈ Review general thermodynamics Chapter 2. Fuel Cell Thermodynamics 2.2. 연료의 열 퍼텐셜 : 반응 엔탈피 √ 엔탈피 미분식 식 (2.22) (2.27) √ 정압과정 (dp = 0), 식 (2.27) : (2.28) ☞ 정압 상태에서 dH 를 dU 의 형태로 표현 : (2.29) ☞ 연소열 : 연소반응과 관련된 엔탈피 변화 반응 엔탈피, 반응열 : 화학반응에서 엔탈피 변화

반응 엔탈피의 계산 Chapter 2. Fuel Cell Thermodynamics ◈ 반응 엔탈피 계산 √ 표준상태에서 형성 엔탈피 : 표준상태에서 1mol 의 화학물ｉ를 만드는 데 필요한 엔탈피 일반적인 반응식 : (2.30) ☞ : 표준상태에서 형성 엔탈피 (2.31) ◈ 예제 2.1 직접메탄올 연료전지 : 엔탈피 엔트로피 계산

엔탈피의 온도 의존성 Chapter 2. Fuel Cell Thermodynamics ◈ 엔탈피 (H) 와 엔트로피 (S) √ The variation of enthalpy with temperature is described by a substance's heat capacity: (2.35) (2.36) √ In a similar manner, this variation is described by the substance’s heat capacity:

2.3. Work Potential of A Fuel Cell Chapter 2. Fuel Cell Thermodynamics Calculating Gibbs Free Energies √ Recalling how G is defined, it is apparent that G already contains H, since G = U + PV – TS and H = U + PV. (2.37) ◈ Gibbs free energy (G) ☞ Differentiating this expression gives (2.38) √ Holding temperature constant (isothermal process) (2.39)

Chapter 2. Fuel Cell Thermodynamics Relationship Between Gibbs Free Energy and Electrical Work ◈ Gibbs free energy (G) & Electrical work (W) √ From Equation 2.17, remember that we define a change in Gibbs free energy as: (2.47) ☞ Include both mechanical work and electrical work: (2.48) ☞ Which yields dG as (2.49)

Chapter 2. Fuel Cell Thermodynamics ☞ For a constant-temperature, constant-pressure process (dT, dp = 0) (2.50) Relationship Between Gibbs Free Energy and Electrical Work ☞ For a reaction using molar quantities (2.51) Where,

Chapter 2. Fuel Cell Thermodynamics Relationship Between Gibbs Free Energy and Reaction Spontaneity ◈ Gibbs free energy (G) & Reaction Spontaneity √ The sign of ∆G indicates whether or not a reaction is spontaneous: ☞ If ΔG is zero, then no electrical work can be extracted from a reaction. ☞ If ΔG is greater than zero, then work must be input for a reaction to occur.

Chapter 2. Fuel Cell Thermodynamics Relationship Between Gibbs Free Energy and Voltage ◈ Gibbs free energy (G) & Voltage (V) √ The electrical work is (2.52) √ If the charge is assumed to be carried by electrons (2.53) ☞ Combining Equations 2.51, 2.52, and 2.53 yields (2.54)

Chapter 2. Fuel Cell Thermodynamics Relationship Between Gibbs Free Energy and Voltage √ For example, in a hydrogen-oxygen fuel cell, the reaction (2.55) ∵ Gibbs free energy charge of -237kJ/mol (standard state conditions for liquid water) ☞ The reversible voltage generated by a hydrogen-oxygen fuel cell under standards-state conditions is thus (2.56)

Chapter 2. Fuel Cell Thermodynamics Standard Electrode Potentials: Computing Reversible Voltages ◈ Computing reversible voltages √ Standard electrode potential tables compare the standard-state reversible voltag- es of various electrochemical half reactions relative to the hydrogen reduction reaction. √ The standard-state potential of hydrogen reduction reaction is defined as zero, thus making it easy to compare other reactions. √ To illustrate the concept of electrode potentials (Table 2.1) √ A more complete set of electrode potentials is provided in Appendix C √ To find the standard-state voltage produced by a complete electrochemical sys- tem, we simply sum all the potentials in the circuit: (2.57)

Chapter 2. Fuel Cell Thermodynamics Standard Electrode Potentials: Computing Reversible Voltages Electrod ReactionE 0 (V) Fe e - ⇌ Fe CO 2 + 2H + +2e - ⇌ CHOOH (aq) H + +2e - ⇌ H CO 2 + 6H + + 6e - ⇌ CH 3 OH + H 2 O 0.03 O 2 + 4H + + 4e - ⇌ 2H 2 O Table 2.1. Selected List of Standard Electrode Potentials

Chapter 2. Fuel Cell Thermodynamics √ For example, the standard-state potential of the hydrogen-oxygen fuel cell is de- termined by Standard Electrode Potentials: Computing Reversible Voltages ☞ Multiply the O2 reaction by ½ to get correct stoichiometry ☞ Do not multiply the E 0 values by ½. ⇒ the E 0 values are independent of reaction amount.

Chapter 2. Fuel Cell Thermodynamics 2.4. Predicting Reversible Voltage of A Fuel Cell Under Non- Standard-State Conditions ◈ Predicting reversible voltage √ In the following sections, we systematically define how reversible fuel cell vol- tage are affected by departures from the standard state. 1. The influence of temperature 2. The influence of pressure ⇒ delineated "Nernst Equation" 3. Contributions from species activity √ Thermodynamic tools to predict the reversible voltage of a fuel cell any arb- itrary set of conditions

Chapter 2. Fuel Cell Thermodynamics Reversible Voltage Variation with Temperature ◈ Reversible voltage variation with temperature √ To understand how to reversible voltage varies temperature. √ Original differential expression for the Gibbs free energy: (2.63) ☞ From which we can write (2.64) ☞ For molar reaction quantities, this becomes: (2.65)

Chapter 2. Fuel Cell Thermodynamics √ We have previously shown that the Gibbs free energy is related to the reversible cell voltage by (2.66) Reversible Voltage Variation with Temperature √ Combining Equations 2.65 and 2.66 (2.67) √ At constant pressure, E T can be calculated by (2.68)

Chapter 2. Fuel Cell Thermodynamics √ As Equations 2.68 indicated 1. △ ŝ(chemical reaction is positive) → will increase with temperature 2. △ ŝ(chemical reaction is negative) → will decrease with temperature Reversible Voltage Variation with Temperature √ For example, consider our familiar H 2 -O 2 fuel cell. (∆ŝ rxn = J/(mol·K) (for H 2 O (g) as product)) (2.69) ∴ Thus, for every 100 degrees increase in cell temperature, there is an appro- ximate 23-mV decrease in cell voltage.

Chapter 2. Fuel Cell Thermodynamics Reversible Voltage Variation with Temperature Figure 2.4. Reversible voltage (ET) versus temperature for electrochemical oxidat- ion of a variety of fuels.

Chapter 2. Fuel Cell Thermodynamics Reversible Voltage Variation with Pressure ◈ Reversible voltage variation with pressure √ Like temperature effects, the pressure effects on cell voltages may also be calc- ulated starting from the differential expression for the Gibbs free energy : (2.70) ☞ This time, we note (2.71) ☞ Written for molar reaction quantities, this becomes (2.72)

Chapter 2. Fuel Cell Thermodynamics ☞ We have previously shown that the Gibbs free energy is related to the reve- rsible cell voltage by (2.73) ☞ Substituting this equation into Equation 2.72 allows us to express how the reversible cell voltage varies as a function of pressure: (2.74) Reversible Voltage Variation with Pressure ⇒ The variation of the reversible cell voltage with pressure is related on the vo- lume change on the reaction.

Chapter 2. Fuel Cell Thermodynamics Reversible Voltage Variation with Pressure √ Usually, only gas species produce an appreciable volume change. Assuming the ideal gas law applies, we can write Equation 2.74 as (2.75) Where, √ Pressure, like temperature, turns out to have a minimal effect on reversible vol- tage.

Chapter 2. Fuel Cell Thermodynamics Reversible Voltage Variation with Concentration: Nernst Equation ◈ Chemical potential (µ) √ Chemical potential (2.76) Where, √ Chemical potential is related to concentration through activity a: (2.77) Where,

Chapter 2. Fuel Cell Thermodynamics Reversible Voltage Variation with Concentration: Nernst Equation √ The activity of a species depends of its chemical nature: ◈ Gibbs free energy (G) √ Combining Equations 2.76 and 2.77, it is possible to calculate changes in the Gibbs free energy for a system of i chemical species by (2.78)

Chapter 2. Fuel Cell Thermodynamics Reversible Voltage Variation with Concentration: Nernst Equation √ Consider an arbitrary chemical reaction placed on a molar basis for species A in the form (2.79) (2.80) (2.81) ∴ This equation, called the van’t Hoff isotherm, tell how the Gibbs free energy of a system changes as a function of the activities (read concentration or gas pressures) of the reactant and product species.

Chapter 2. Fuel Cell Thermodynamics Reversible Voltage Variation with Concentration: Nernst Equation √ From previous thermodynamic explorations (Section 2.3.4), we know that the Gibbs free energy and the reversible cell voltage are related: (2.82) √ Combining Equations 2.81 and 2.82 (2.83) √ The general form of Nernst equation (2.84) ◈ Nernst equation

Chapter 2. Fuel Cell Thermodynamics Concentration Cell √ In a concentration cell, the same chemical species is present at both electrodes but at different concentrations. √ Electrochemical potential (2.93) Where, : the electrochemical potential of species : the chemical potential of species : the charge number on the species : Faraday’s constant : the electrical potential experienced by species

Chapter 2. Fuel Cell Thermodynamics Concentration Cell Figure 2.5. hydrogen concentration cell. A high-pressure hydrogen compartment and a low pressure hydrogen compartment are separated by a platinum- electrolyte-platinum membrane structure. This device will develop a voltage due to the difference in the chemical potential of hydrogen bet- ween the two compartments.

Chapter 2. Fuel Cell Thermodynamics Summary √ Briefly summarize the effects of nonstandard-state conditions on reversible ele- ctrochemical cell voltages. ☞ The variation of the reversible cell voltage with temperature is ☞ The variation of the reversible cell voltage with pressure is ☞ The variation of the reversible cell voltage with chemical activity (chemical composition, concentration, etc.) is given by the Nernst equation: (2.98) (2.99) (2.100)

Chapter 2. Fuel Cell Thermodynamics 2.5. Concentration Cell √ A real fuel cell must always be less efficient than an ideal fuel cell because real fuel cells incur nonideal irreversible losses during operation Ideal Reversible Fuel Cell Efficiency √ Define the efficiency ε (2.101) (2.102) √ Carnot cycle.

Chapter 2. Fuel Cell Thermodynamics Ideal Reversible Fuel Cell Efficiency

Chapter 2. Fuel Cell Thermodynamics Real (Practical) Fuel Cell Efficiency √ As mentioned previously, the real efficiency of a fuel cell must always be less than the reversible thermodynamic efficency. The two major reasons are as follows: 1. Voltage losses 2. Fuel utilization losses √ The real efficiency of a fuel cell,, may be calculated as √ efficiency of a real fuel cell as (2.107) (2.111)

Chapter 2. Fuel Cell Thermodynamics Chapter Summary The purpose of this chapter is understand the theoretical limits to fuel cell performance by applying the principles of thermodynamics. The main points introduced in this chapter include the following: √ Thermodynamics provides the theoretical limits or ideal case for fuel cell perfor- mance. √ The heat potential of a fuel is given by the fuel's heat of combustion or, more generally, the enthalpy of reaction. √ Not all of the fuel is given by the Gibbs free energy, ΔG. √ Electrical energy can only be extracted from a spontaneous ("downhill") chemical reaction. The magnitude of ΔG gives the amount of energy that is available ("fr- ee") to do electrical work. Thus, the sign of ΔG indicates whether of not electrical work can be done, and the size of ΔG indicates how much electrical work can be done. √ The reversible voltage of a fuel cell, E, is related to the molar Gibbs free energy by. √ ΔG scales with reaction amount whereas and. E do not scale with reaction amount.

Chapter 2. Fuel Cell Thermodynamics Chapter Summary √ E varies with temperature as. For fuel cells, is generally negative, therefore reversible fuel cell voltages tend to decrease whit increasing temperature. E varies whth pressure as : √ The Nernst equation describes how E varies with reactant/product activites: √ The Nernst equation intrinsically includes the pressure effects on reversible cell voltage but does not fully account for the temperature effects. √ Ideal HHV fuel cell efficiency √ Thermodynamic fuel cell efficiency generally decreases as temperature increases. Contrast this to heat engines, for which thermodynamic efficiency generally incr- eases as temperature increases. √ Real fuel cell efficiency is always less than the ideal thermodynamic efficiency. Major reasons are irreversible kinetic losses and fuel utilization losses. Total overall efficiency is given by the product of individual efficiencies.