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