57 lines
2.7 KiB
ReStructuredText
57 lines
2.7 KiB
ReStructuredText
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************************************
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Chemical Equilibrium Example Program
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************************************
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In the program below, the `equilibrate` method is called to set the gas to a
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state of chemical equilibrium, holding the temperature and pressure fixed.
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.. literalinclude:: demoequil.cpp
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:language: c++
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The program output is::
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temperature 1500 K
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pressure 202650 Pa
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density 0.316828 kg/m^3
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mean mol. weight 19.4985 amu
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1 kg 1 kmol
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----------- ------------
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enthalpy -4.17903e+06 -8.149e+07 J
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internal energy -4.81866e+06 -9.396e+07 J
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entropy 11283.3 2.2e+05 J/K
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Gibbs function -2.1104e+07 -4.115e+08 J
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heat capacity c_p 1893.06 3.691e+04 J/K
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heat capacity c_v 1466.65 2.86e+04 J/K
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X Y Chem. Pot. / RT
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------------- ------------ ------------
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H2 0.249996 0.0258462 -19.2954
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H 6.22521e-06 3.218e-07 -9.64768
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O 7.66933e-12 6.29302e-12 -26.3767
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O2 7.1586e-12 1.17479e-11 -52.7533
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OH 3.55353e-07 3.09952e-07 -36.0243
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H2O 0.499998 0.461963 -45.672
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HO2 7.30338e-15 1.2363e-14 -62.401
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H2O2 3.95781e-13 6.90429e-13 -72.0487
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AR 0.249999 0.51219 -21.3391
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How can we tell that this is really a state of chemical equilibrium? Well, by
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applying the equation of reaction equilibrium to formation reactions from the
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elements, it is straightforward to show that:
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.. math:: \mu_k = \sum_m \lambda_m a_{km}.
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where :math:`\mu_k` is the chemical potential of species *k*, :math:`a_{km}` is
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the number of atoms of element *m* in species *k*, and :math:`\lambda_m` is the
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chemical potential of the elemental species per atom (the so-called "element
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potential"). In other words, the chemical potential of each species in an
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equilibrium state is a linear sum of contributions from each atom. We see that
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this is true in the output above---the chemical potential of H2 is exactly
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twice that of H, the chemical potential for OH is the sum of the values for H
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and O, the value for H2O2 is twice as large as the value for OH, and so on.
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We'll see later how the :ct:`equilibrate <Cantera::ThermoPhase::equilibrate>`
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function really works.
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