INDUSTRIAL ECOLOGY OF EARTH RESOURCES (EAEE E4001)
WEEK 12B: SOME USEFUL THERMODYNAMIC CONCEPTS
Enthalpy, H, of a chemical species: Sensible heat in the material (Cp dT)+ chemical heat of formation
of compound (e.g. H20) + heat of physical transformation (e.g. ice to liquid water); all expressed in Joules
per gram or kilogram of material. In the case of a reaction, enthalpies of products – enthalpies of reagents =
heat of reaction. Convention used: Exothermic reaction (generates heat), negative sign; endothermic heat
(absorbs heat, positive sign. (1st law of thermodynamics: conservation of energy)
(e.g , for reaction: H2 + 0.5 O2 = H2O
Hreaction=HH2O - (HH2 + 0.5HO2)
Entropy, S, of a reversible process (e.g. melting of ice to water; freezing of water to ice):
The amount of heat absorbed during the process (e.g. melting of ice) divided by the absolute temperature
at which the process took place (e.g. for ice melting, 273K).
S= H/T
(2nd law of thermodynamics: The total entropy change in a system resulting from a any real process in the
system is positive and approaches a limiting value of zero for any process that approaches reversibility.)
At 0 K, the entropy of all elements and compounds is zero.
Free energy of formation, G, of a chemical species or reaction:
In chemical thermodynamics, the enthalpy and the entropy of elements and compounds are expressed
as the differences of these quantities from a reference temperature (usually 298.15K), AH andAS.
The Gibbs free energy of an element or compound. It is computed from the enthalpy and entropy terms:
G = H – T S
For example, if we want to know if a particular reaction of reagents A and B will proceed to form products C
and D, we can add the free energies of C and D, and subtract the sum of the free energies of A and B. If
the result is a negative number, the reaction will proceed spontaneously to form products C and D. On the
contrary, a positive number would indicate that this reaction is not thermodynamically favored. The
thermodynamic equilibrium between reagents and products is a function of the free energy of the reaction.
Consider the reaction between metallic iron and atmospheric oxygen to form iron oxide:
2Fe + 1.5 O2 = Fe2O3
You can look up any thermodynamic table and you will find that the free energy of formation of iron oxide at
near-room temperatures is much greater than the free energies of metallic iron and oxygen. That’s why a
piece of iron exposed to the atmosphere for long periods of time will rust. That’s why nearly all the iron
mined at this time is in the form of iron oxides. If we want to bring the iron to its metallic state, we need to
react it with some element or compound such that the free energy of the reducing reaction will be negative,
e.g.
Fe2O3 +3H2 = 2Fe + 3H 2O
Every physical and chemical transformation of materials involves a change in enthalpy and entropy,
therefore in free energy.
Theoretically every chemical reaction can proceed forward or backward (reversible reaction). For example,
In the reduction of iron oxide, the equilibrium constant for the reaction is expressed in terms of the free
energy of the reaction as follows:
K e =([H 2O]3 [Fe]2 ) / ([H2]2[Fe2O3]) = e- G/RT
where [H2O], etc. represent the activity of [H2O], etc. of all reagents and products. In this case, the activities
of the solids (Fe, Fe2O3) can be assumed to be equal to 1 while the activities of the two gases are equal to
their respective concentrations in the atmosphere around the oxide/metal system; T is the absolute
temperature of the reaction, R the universal gas constant (=8.314E+03 J kmol/K) and G the free energy of
the reaction, calculated by adding the free energies of the products and subtracting the free energies of the
reagents (in the same way as the Hreaction , above).
Introduction to class of the chemical thermodynamics program HSC Chemistry (available from
Outokumpu Research; Pori, Finland)
CONCEPT OF “EXERGY”
Connelly and Koshland (Exergy-based measures) pointed out that in defining consumption it is not
sufficient to consider only the rate of consuming materials but also the degree of degradation that the
consumed materials are subjected due to consumption. Therefore, they introduced the concept that
consumption rate should be the product of two quantities:
Consumption rate = (material consumed/time) * (degradation (loss of quality)/unit mass).
It is relatively easy to quantify the first quantity but extremely difficult to express “degradation”. We cannot
use economic value because it depends on supply/demand at a particular period in time. Therefore,
Connelly et al proposed to use the 2nd law of thermodynamics and introduce a thermodynamic property
called “exergy”. According to this model, “exergy measures the useful energy content of a substance –i.e.,
energy that may be used to perform work at 100% efficiency - relative to a specified thermodynamic
ground-state) and is applicable to “energy” resources such as fossil fuels and “waste” heat and also to
material resources, such as iron ore, iron and fuel oil.
Another definition given of exergy is
“the minimum quantity of useful energy that was used to bring that material from a specified ground
state to its current state”
It should be noted that “exergy” is not a conserved property of the material: it may be removed from a
resource by transfer to another or by loss, i.e. complete destruction of the material. Also, “an important
property of exergy is that the amount lost from a resource during any form of consumption must later on be
transferred to the consumed material from another resource in order to return it to its pre-consumption
state”.
Let us examine what is the relationship of the proposed “exergy” to the well established property of “free
energy” on which is based most of the current industrial production of materials. To do so, we will consider
two well known and important primary materials: Iron ore and petroleum.
Exergy Case 1: Iron ore
As discussed at the beginning of these notes, iron ores consist of iron oxides intermingled in nature with
other oxides, such as silica, magnesia, calcia and alumina. Also, in order to get to the iron ore, a certain
amount of overburden or waste ore must be mined and set aside. Once the ore is brought to the surface it
is subjected to crushing, grinding and physical separation of the rich iron grains from the other oxides. We
can compute the total “stored” exergy per kilogram of iron contained in the ore by adding to the chemical
free energy of the oxide (-7,613 kJ/kg Fe), the free energy terms that correspond to the work done in mining
and concentrating the iron ore (i.e., the entropy increase in the mining and concentrating system in order to
decrease the disorder prevailing in the original deposit of iron oxides); let us assume that they amount to
50% of the chemical free energy, i.e. -3,806 kJ/kg Fe.
The iron ore is next smelted with carbon and oxygen in a smelting furnace and then refined to steel in an
oxygen refining furnace, both of which were discussed earlier in this course. As a result of these
operations, the free energy of the iron in the steel metal produced is only -145 kJ/kg Fe. However, the
reduction in free energy of contained iron has taken place at the expense of using about one ton of coal per
ton of iron and some electrical power. Therefore, the “stored” exergy in the iron metal produced has
increased to at least -11,564 kJ/kg.
Let us now follow the steel in the manufacturing process and through the life of the steel products. Any
“adulteration” of the metal with other materials, such as plastics, other metals, paints will increase its free
energy and will require more energy input, from use of other materials, to bring it back to the pristine state
of metal as it left the steel mill. The highest chemical content in the solid state will be reached for fully
corroded metal. The “stored” exergy will be much greater for iron oxide dissolved in water. Also, it will be
practically infinite, per unit mass of iron, for corroded particles dispersed over land and water, or for steel
waste discarded irretrievably in landfills.
Exergy Case 2: Petroleum
As in the case of iron ore, the free energy of gasoline from oil consists of the chemical free energy of the
hydrocarbons in the oil, plus the “stored” free energy of producing and refining the oil. For octane, the
chemical free energy is only -3,137 kJ/kg of gasoline. When this fuel is combusted with oxygen, the
principal reaction can be represented as
C8H18 + 12.5 O2 = 8CO2 + 9H2O
The free energy that is made available by this reaction, is enormous in comparison to the free energy of
octane: About -46,455 kJ are released per kilogram of gasoline are released. The free energy in CO 2 and
H2O is irretrievable because there are no elements or compounds that can be reacted usefully with CO2 ; in
any case, both CO2 and H2O are plentiful in nature. Therefore, when the gasoline is used up in an
automobile engine, none of the free energy of the above combustion is “stored”.
Comparison of “exergy” and “free energy”
The term “exergy” is equivalent to the Gibbs free energy with a minus sign in front. The example of
methanol solutions in water is a clear indication of the meaning of exergy: As the concentration of alcohol in
water decreases (and its entropy increases), the free energy of solution increases. So does the exergy term
computed as per the C and K concept. In summary, the term “exergy” is not a substitute for the
scientifically rigorous term of free energy, which represents the total chemical energy stored in materials.
However, as illustrated by the above examples, it is a useful concept to denote
the negative value of the sum of free energies actually stored within the material + the sum of free energies
generated by all external reactions and systems involved to produce this material.
Good luck with your term papers!