NTU ME

H.K. MaDepartment of Mechanical Engineering National Taiwan University, Taipei, Taiwan

November, 2009

台灣大學機械工程系能源環境實驗室

Maximum electric work (Wel) at constant temp. and pressure is given by Gibbs free energy:

• n is no. of electrons • F is Farady’s constant• E is ideal potential of the cell

Besides, Gibbs’ free energy can be written as:

• ∆H is enthaply change

• ∆S is entropy change

• T∆S represents the unavailable energy resulting from the entropy change

At constant pressure, the specific entropy at temperature T is given by

It than follows that,

The Gibbs’ free energy can be expressed by the equation

• For the generation reaction,

• Substituting the equation

into then,

This is general form of the Nernest Equation

NTU ME

NTU ME

NTU ME

The ideal efficiency of a fuel cell, operating reversibly, is then,

• At standard condition (298K, 1atm), thermal energy (∆H ) in the hydrogen/oxygen reaction is 285.8KJ/mole, and the free energy for useful work is 237KJ/mole, therefore,

The thermal efficiency of a hydrogen/oxygen can be written in term of the actual cell voltage

Activation losses are caused by sluggish electrode kinetics. It is possible to approximate the voltage drop by a semi-empirical equation, called the Tafel equation.

• α is the electron transfer coefficient of the reaction at the electron being addressed

• i0 is the exchange current density

Ohmic losses occur because of resistance to the flow in the electrolyte and resistance to the flow electrons through the electrode.

Because the electrolyte and fuel cell electrodes obey Ohm’s law, the ohmic losses can be expressed by the equation,

The total resistance, R, which includes electronic, ionic, and contact resistance

The combined effect of the losses for a given cell and given operating conditions can be expressed as polarizations. The total polarization at the electrode is the sum of anode and cathode.

The cell voltage includes the contribution of the anode and cathode potentials and ohmic polarization

• When and

are substituted in then,

19

AFC PEMFC DMFC PAFC MCFC SOFC

Ion OH- H+ H+ H+ CO-23

O-2

Temperature 50~200℃ 30~120℃ 20~90℃ ~220℃ ~650℃ 500~1000℃

Fuel H2 H2 CH3OH H2 NG, H2… NG, H2…

Oxides O2 O2 O2 O2 O2 O2

Output (W) 1KW~10K 1~100K 1~100 10K~1M 1M~10M 1K~10M

112/04/21

20

Water product T (K) E (V)

Liquid 298 1.23

Liquid 353 1.18

Gas 373 1.17

Gas 473 1.14

Gas 673 1.09

Gas 873 1.04

Gas 1273 0.92

nFEGWele .

OHOH 222 21

222)()()( OHOH GGGG

sThG

EmolVJ

molKJnFEG

/964722

/2.237

VE 23.1112/04/21

21

Volume flow rate

H2 6.964 cc/min.

O2 3.483 cc/min.

Air 16.586 cc/min.

.min1/.sec60/2/144.96472//1.sec1/12

electronmolemolegCelectronmoleCVH

eHH 222

molgLmolegmoleg 1/4.22min/10109.3.]min/[10109.3 44

.min/..964.6.]min/[10964.6 4 ccL

.min/10268.61/1016.2.]min/[10109.3 44

2gmoleggmolgmH

.min/10555.1

2/1.min/10109.34

4

2222

moleg

molegmolegmolegn HOHO

.]min/..[483.3

.min/10483.3)1/(4.22.min/10555.1 34

2

cc

LmolegLmolegVO

]/[10567.3min]/[021.01/9.28

21.0/1.min/10555.14

4

22

sggmolegg

molegmolegmolegm

airair

OairOair

112/04/21

22

Water product T (K) Efficiency limit (%)

Liquid 298 83

Liquid 353 80

Gas 373 79

Gas 1273 62

1

21T

TT

Efficiency of fuel cell = electric energy produced per mole of fuel / enthalpy of formation

Limit of fuel cell efficiency =)(HHVf

f

hg

Carnot Limit=

Thermodynamic efficiency112/04/21

Reactant

Product

Reactant Product

Energy Barrier

Reaction Rate

112/04/21 23

Activation losses:

0log i

iAVact

Ohmic losses:

iRVohmicConcentration losses:

11ln2 i

iF

RTVtrans

112/04/21 24