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Modern Engineering Thermodynamics

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636 CHAPTER 15: Chemical <strong>Thermodynamics</strong><br />

From Eq. (11.8), we have the relation dg = vdp− sdT, so that, for a constant pressure process, we can write<br />

d g • i<br />

dT = −s• i<br />

Introducing this result along with the definition of the molar specific Gibbs function, g = h − T s, into the equation<br />

for dK e /dT and rearranging gives<br />

or<br />

1<br />

K e<br />

<br />

dK e<br />

dT<br />

= dð ln K eÞ<br />

dT<br />

= − 1<br />

RT 2<br />

∑<br />

R ′<br />

The van’t Hoff equation:<br />

dð ln K e Þ<br />

dT<br />

!<br />

v i h • i −∑ v i h • Q<br />

i = _ r<br />

RT<br />

P 2<br />

′<br />

= _ Q r<br />

RT 2 (15.39)<br />

where _Q r istheheattransferrateofthereaction. This equation is known as the van’t Hoffequation.Itshows<br />

that, for a heat-producing (i.e., exothermic) reaction, the value of K e decreases when the reaction temperature<br />

increases and increases when the reaction temperature decreases. While for a heat-absorbing (i.e., endothermic)<br />

reaction, the value of K e increases when the temperature of the reaction increases and decreases when the reaction<br />

temperature decreases. Since the equilibrium constant is a relative measure of the amount of product present,<br />

by changing the reaction temperature, we can change the amount of product formed. For example,<br />

consider the equilibrium equation for the formation of ammonia from hydrogen and nitrogen gas,<br />

N 2 + 3ðH 2 Þ ⇆ 2ðNH 3 Þ − 91:25 kJ. We can increase the amount of ammonia produced by increasing the K e of the<br />

reaction. Since the reaction is exothermic, this can be done by lowering the reaction temperature.<br />

15.15 FUEL CELLS<br />

The highly inefficient heat engine energy conversion technology that provided<br />

the mobile power for the technological developments of the 17th<br />

through the 20th centuries is coming to an end. The thermal combustion of<br />

chemical fuel to propel the heat engines of the past has come to be the<br />

source of numerous worldwide social problems today. Chemical<br />

and thermal pollution of the Earth’s air and water plus a continuously diminishing<br />

supply of suitable fuels is clearly signaling the end of the heat engine<br />

era. But, what other, less ecologically damaging energy conversion technologies<br />

do we have to support the societies of the next few centuries?<br />

What about electrical batteries? Technically, a battery consists of two or<br />

more electrochemical cells that convert chemical energy directly into electrical<br />

energy. The term battery, however, is often used to describe a single cell.<br />

Figure 15.12 illustrates the basic elements of an electrochemical cell.<br />

Ordinary commercial batteries are closed systems because no mass crosses<br />

their boundaries; consequently, as they are used, they consume their stored<br />

electrical energy and become discharged. If the electrolyte needed to operate<br />

the cell were continuously supplied from outside the cell, then it would<br />

become an open system and would never become discharged. Such an open<br />

system electrochemical cell is called a fuel cell.<br />

Since a fuel cell (Figure 15.13) does not produce heat as its primary energy<br />

conversion mode, it is therefore not a heat engine. Consequently, fuel cells<br />

are not subject to the severe limitation of the Carnot (heat engine) efficiency,<br />

and fuel cell efficiencies can approach 100% under the proper conditions.<br />

Consider a general steady state, steady flow, open system. Neglecting any<br />

changes in kinetic or potential energy, the energy rate balance on this system<br />

gives its work transport rate of energy (i.e., power) as<br />

_W = ∑<br />

in<br />

_m i h i −∑<br />

out<br />

_m i h i + _Q = ∑<br />

in<br />

_n i h i −∑ _n i h i + _Q<br />

out<br />

Current<br />

e+ e−<br />

Electrons<br />

−<br />

+<br />

Electrodes<br />

Electrolyte<br />

FIGURE 15.12<br />

The operation of a basic electrochemical<br />

cell using one electrolyte. Electrical<br />

current is the time rate of change of<br />

electrical charge, originally defined by<br />

Benjamin Franklin to flow from the<br />

positive to the negative terminal.<br />

However, since electrons are the charge<br />

carriers for current in conductors and the<br />

charge of an electron is negative, the<br />

direction of electron flow is actually from<br />

the negative to the positive terminal.<br />

Nonetheless, we maintain the old<br />

concept of current flow from positive to<br />

negative and call this the conventional<br />

flow notation.

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