B. PROSPECTO
6. Contenido del envase e información adicional Composición de Entyvio
When reacting systems are under consideration, the same basic problem arises for entropy as for enthalpy: A common datum must be used to assign entropy values for each substance involved in the reaction. This is accomplished using the third law thermodynamics, which deals with the entropy of substances at the absolute zero of temperature. Based on experimental observations, this law states that the entropy of a pure crystalline substance is zero at the ab- solute zero of temperature, 0 K or Substances not having a pure crys- talline structure at absolute zero have a nonzero value of entropy at absolute zero. The experimental evidence on which the third law is based is obtained primarily from studies of chemical reactions at low temperatures and specific heat measurements at temperatures approaching absolute zero.
The third law provides a datum relative to which the entropy of each substance participating in a reaction can be evaluated so that no ambiguities or conflicts arise. The entropy relative to this datum is called the absolute The change in entropy of a substance between absolute zero and any given state can be determined from precise measurements of energy transfers and specific heat data or from procedures based on statistical
and observed molecular data.
When the absolute entropy is known at the standard state, the specific entropy at any other state can be found by adding the specific entropy change between the two states to the absolute entropy at the standard state. Similarly, when the absolute entropy is known at the pressure and temperature the absolute entropy at the same temperature and any pressure can be found from
(2.70) The term in brackets on the right side of Equation 2.70 can be evaluated for an ideal gas by using Equation 2.47, giving
p ) = - - P (ideal gas) (2.71)
In this expression, denotes the absolute entropy at temperature T and pressure
The entropy of the kth component of an ideal-gas mixture is evaluated at the mixture temperature T and the partial pressure The partial
2.4 REACTING MIXTURES AND COMBUSTION 81
pressure is given by = where is the mole fraction of component k and p is the mixture pressure. Thus, for the kth component of an ideal-gas mixture Equation 2.7 takes the form
or
(component k of an ideal-gas mixture)
(2.72)
where is the absolute entropy of component k at temperature T and The molar Gibbs function is
(2.73) For reacting systems, values for the Gibbs function are commonly assigned in a way that closely parallels that for enthalpy: A zero value is assigned to the Gibbs function of each stable element at the standard state. The Gibbs of a compound equals the change in the Gibbs function for the reaction in which the compound is formed from its elements. The Gibbs function at a state other than the standard state is found by adding to the Gibbs function of formation the change in the specific Gibbs function
between the standard state and the state of interest:
The Gibbs function of component k in an ideal-gas mixture is evaluated at the partial pressure of the component and the mixture temperature.
2.4.4 Ancillary Concepts
Table Data. Property data suited for the analysis of reactive systems are available in the literature Tables giving standard state values of the enthalpy of formation, absolute entropy, and Gibbs function of formation in SI and English units are provided in Reference for the specification =
82 THERMODYNAMICS, MODELING, AND DESIGN ANALYSIS
1 atm. This source also provides versus temperature for several gases mod- eled as ideal gases. Values for specific heat, enthalpy, absolute entropy, and Gibbs function are given in Reference 6 versus temperature for = 1 bar.
Reference 6 also provides simple analytical representations of these thermo- chemical functions readily programmable for use with personal computers.
See Table C.l in Appendix C for a sampling; in this table, the behavior of the gases corresponds to the ideal-gas model.
Maximum Work. To illustrate the combustion principles introduced thus far, let consider the maximum work per mole of fuel that can be developed by the system shown schematically in Figure 2.3. The result, Equation 2.75, is applied in Section 3.4.3. The system considered in this development is similar to such idealized devices as a reversible fuel cell or a van't Hoff equilibrium box. Referring to Figure 2.3, a hydrocarbon fuel and oxygen 0, enter the system in separate streams; carbon dioxide and water exit sep- arately. All entering and exiting streams are at the same temperature T and pressure p . The reaction is complete:
+
(a+ - +
The derivation of Equation 2.75 parallels that of Equation 2.27: For steady- state operation, the energy rate balance for the system reduces to give on a per mole of fuel basis
=
- +
-+
(a+
- ah,,, -Figure 2.3 Device for evaluating maximum work.
2.4 REACTING MIXTURES AND COMBUSTION 83 where the subscript F denotes fuel. Kinetic and potential energy effects are regarded as negligible. If heat transfer occurs only at temperature an en- tropy balance for the control volume takes the form
+
+
(a+
- -+
-T
Eliminating the heat transfer term from these expressions, the work developed per mole of fuel is
In this expression, the enthalpies would be evaluated in terms of enthalpies of formation via Equation 2.69 and the entropies are necessarily absolute entropies. An expression for the maximum value of the work developed per mole of fuel, corresponding to the absence of irreversibilities within the sys- tem, is obtained when the entropy generation t e m is set to zero:
Referring to the discussion of enthalpy of combustion given previously in this section, the term in curly brackets on the right side of Equation is recognized as Thus, Equation can be written as
When the temperature and pressure in this expression correspond, respec- tively, to 25°C (77°F) and 1 bar (or 1 atm), the term corresponds to the standard heating value: the higher heating value, when water exits the system of Figure 2.3 as a liquid, and the lower heating value, LHV, when water vapor exits.
Alternatively, using the specific Gibbs function = - Equation can be expressed in the form
THERMODYNAMICS, MODELING, AND DESIGN ANALYSIS
Reaction Equilibrium. Consider a system at equilibrium containing five components, A, B, C, D, and E, at a given temperature and pressure, subject to a chemical reaction of the
+ +
where the are stoichiometric coefficients. Component E is assumed to be inert and thus does not appear in the reaction equation. The form of the equation suggests that at equilibrium the tendency of A and to form and D is just balanced by the tendency of C and D to form A and B.
At equilibrium, the temperature and pressure would be uniform throughout the system. Additionally, the following expression, called the equation of reaction equilibrium, must be satisfied [
where the p’s are the chemical potentials (Section 2.3.2) of A, B, C, and in the equilibrium mixture. In principle, the composition that would be present at equilibrium for a given temperature and pressure can be determined by solving this equation. The solution procedure is simplified by using the equi- librium constant defined by
(2.77)
where
As before, the superscript degree symbol denotes properties at Further discussion of the equilibrium constant is provided in Reference 1.