Page 230 - Advanced thermodynamics for engineers

10.4 APPLICATION OF THE ENERGY EQUATION 217

processes cease to be identical and, in the case of a combustion bomb, a piston would have to move to
maintain the conditions. The movement of the piston produces work equal to <T (n P –n R ).
It is also possible to relate the quantity of energy that is chemically bound up in the fuel to a value at
absolute zero of temperature. These values are denoted as DH 0 and DU 0 and will be returned to later.

10.4.3 HEAT OF FORMATION – HESS’S LAW
The heat of formation of a compound is the quantity of energy absorbed (or released) during its
formation from its elements (the end pressures and temperatures being maintained equal).
For example, if CO 2 is formed from carbon and oxygen by the reaction

C þ O 2 /CO 2 (10.14)
then in a constant pressure steady flow process with equal temperature end states, the reaction results in
heat transfer of Q p given by

Q p ¼ H P H R (10.15)
¼ 394 MJ=kmol: (10.16)
If a slightly different reaction is performed giving the same end product, e.g.
1
CO þ O 2 /CO 2 (10.17)
2
then it is not possible to use the same simple approach because the reactants are a mixture of elements
and compounds. However Hess’s law can be used to resolve this problem. This states that:

1. if a reaction at constant pressure or constant volume is carried out in stages the algebraic sum
of the amounts of heat evolved in the separate stages is equal to the total evolution of heat
when the reaction occurs directly;
or
2. the heat liberated by a reaction is independent of the path of the reaction between the initial
and final states.
Both of these are simply statements of the law of energy conservation and the definition of
properties. However, this allows complex reactions to be built up from elemental ones. For example,
the reaction
1
CO þ O 2 /CO 2 (10.18)
2
can be subdivided into two different reactions.
1
C þ O 2 /CO (10.19a)
2
1
CO þ O 2 /CO 2 (10.19b)
2