Thermodynamics Fuel Cells

8/8/2019 Thermodynamics Fuel Cells

1/19

Describing a fuel cells performance and efficiency

Basic energy conversion of a fuel cell was described as:

Chemical energy of fuel = Electrical energy + Heat energy

Fuel Cell

Energy = ? Electricity Energy = VIt

Heat (byproduct)

OxygenEnergy = ?

Water (byproduct)

The input energy is that produced during reactions at the electrodes.In this section we will describe the above ener balance in more detail usinthe first and second laws of thermodynamics.


2/19

Performance (cont.)

The performance of a fuel cell is governed by its Polarization Curve.

Ideal performance

This type of performance curve showsthe DC voltage delivered at the cellterminals as a function of the currentdensity (current per unit area of membrane)

being drawn by the external load.

with its shape will be discussed later.

(ref. 1)

One measure of the energy conversion efficiency of a fuel cell is the ratioof the actual voltage at a given current density to the maximum voltageobtained under no load (open circuit) conditions.


3/19

Thermodynamic Analysis: 1st Law

Control VolumeElectrolyte

Fuel

Oxidant

-E

+E

1st Law for a control volume:

E = Q W where E = KE + PE + U + (PV) = H

For a fuel cell, the work is obtained from the transport of electrons across

=> H = Q - W

a potent a erence, not y mec an ca means, suc as turn ng oturbine blades.


4/19

Defining the work term

Electrical work is, in general, described by the relation: W = EIt

In a fuel cell reaction, electrons are transferred from the anode to the cathode,generating a current. The amount of electricity (It) transferred when thereaction occurs is given by NF, where

N = number of electrons transferred

F = Faradays constant = 96,493 coloumbs

So the electrical work can be calculated as: W = NFE

The First Law then becomes: H = Q - NFE


5/19

Thermodynamic Analysis: 2nd Law

Will consider the fuel cell to be ideal for now, meaning that it is reversible andthus behaves as a perfect electrochemical apparatus (Gibbs):

If no changes take place in the cell except during the passage ofcurrent, and all changes which accompany the current can be reversed byreversin the current the cell ma be called a erfect electrochemicalapparatus.

Recall that the heat transferred during a reversible process was expressed as:

Q = T S

Combining the First and Second Law analysis, we get:

H = TS - NFE


6/19

Gibbs Free Energy (chemical potential)

From our previous result for a cell operating reversibly:

dH = TdS FEdN

Under these conditions: - the losses are minimal-

This maximum work is represented by the Gibbs free energy: dG = -FEdN

So the thermodynamic expression for the maximum useful workobtained from a fuel cell becomes:

= -


7/19

Physical Interpretation of dG = dH - TdS

dH re resents the total ener of the s stem.

TdS represents the unavailable energy (that which cannot beconverted to useful work).

ere ore represen s e ree energy or e energyavailable to do useful work.


8/19

More on Gibbs Free Energy

The electrons released to generate the electrical work are, of course,inherently related to the chemical reaction taking place. So G can alsobe associated with the chemical energy released during the reaction

occurring in the fuel cell.

o, , f reactions, where the free energy is referenced with respect to standardtemperature and pressure (STP) conditions.

For a given reaction, Go = Goproducts Goreactants

See example problem 15.2 for calculation of Go


9/19

Electrochemistry: Fuel Cell Reactions

Hydrogen fuel cell:

x a on a reac on 2 + e-

Reduction half reaction O2 + 4H+ + 4e- 2H2O

Energy formation (kJ/mol)

-Ho -Go____________________________________________Cell reaction 2H2 + O2 2H2O

286 237

Methanol fuel cell:

Cell reaction: CH4 + 2O2 CO2 + 2H2O 890 818


10/19

Maximum Voltage Produced by a Single Cell

The reversible open circuit voltage (i.e. the maximum voltage that couldo

Go

=NF

For example, in the previous reaction where Go was 237 kJ/mol, theopen circuit voltage would be:

E = 237,000(2 mol H2)/(4 electrons)(96,493) = 1.23 volts


11/19

Fuel Cell Vs. Carnot Cycle Efficiency

The efficiency limit of a Carnot heat engine is defined as:

H

L

carnot

T

T=1

So the higher the hot temperature source, the higher the efficiency.

If, for example, one wanted to calculate the maximum efficiency of asteam turbine operating at 400C with the water exhausted through a

,

52.01325

675 ==car

n er ese con ons, e ur ne cou e no more an e c en .


12/19

Fuel Cells Vs. Carnot Engines (cont.)

Fuel cells, on the other hand:

Operate isothermally no temperature cycling.

Operate with less energy lost in maintaining the temperature of thehot source.

Are inherently less irreversible.

Fuel cells are not limited by the Carnot efficiency limit.


13/19

Fuel Cell Efficiency

Since fuel cells use materials that are typically burnt to release theirener , the fuel cell efficienc is described as the ratio of the electrical

energy produced to the heat that is produced by burning the fuel (its

enthalpy of formation or hf).

= in

where W is given by G (or NFE)

Qin is the enthalpy of formation of the reaction taking

place. Since two values can often be computeddepending on the state of the reactant, the larger of

.

NFEG=

=

HHVHHV


14/19

Maximum Fuel Cell Efficiency

The maximum efficiency occurs under open circuit conditions (reversible).

NFEGoo

HHVHHVmax

For the hydrogen fuel cell reactions shown previously whereGo was 237 kJ/mol and Ho was 286 kJ/mol, the maximum efficiencyof the fuel cell would be 83%.


15/19

How does a Carnot engine match up?

A Carnot engine would have to have a high temperature

298 K, to achieve an efficiency of 83%!

However, the work done by a Carnot engine increaseswith increasing temperature.

The reverse is true for the G based fuel cell work (andhence efficiency) because G decreases with increasingtemperature.


16/19

Fuel Cell Vs. Carnot Efficiencies

As can be seen, there exists a temperature above which the fuel cellefficiency is lowerthan the Carnot efficiency. This temperature isapproximately 950 K for a H2-O2 system.


17/19

Losses Associated With Fuel Cell Operation

n rea ty ue ce s ac eve t e r

highest output voltage at opencircuit (no load) conditions andthe volta e dro s off with increasin

current draw. This is known aspolarization.

ref. 2

The polarization curve shows the electrochemical efficiency of the fuel cellat any operating current.


18/19

Classification of Losses in an Actual Fuel Cell3

Activation Losses: These losses are caused by the slowness of the reactiontaking place on the surface of the electrodes. A proportionof the voltage generated is lost in driving the chemical

reaction that transfers the electrons.

through the material of the electrodes. This loss varieslinearly with current density.

oncen ra on osses: osses a resu rom e c ange n concen ra on othe reactants at the surface of the electrodes as thefuel is used.

Fuel Crossover Losses: Losses that result from the waste of fuel passingthrough the electrolyte and electron conduction

through the electrolyte. This loss is typically small,.


19/19

References

1Thomas, S. & Zalbowitz,M. Fuel Cells- Green Power, Los Alamos National Laboratory,http://education.lanl.gov/resources/fuelcells/fuelcells.pdf

2Fuel Cell Technology.pdf

3Larmanie, J. & Dicks, A. 2000 Fuel Cell Systems Explained, John Wiley & Sons.

Thermodynamics Fuel Cells

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