Cantera  3.1.0a1
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MargulesVPSSTP.cpp
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1/**
2 * @file MargulesVPSSTP.cpp
3 * Definitions for ThermoPhase object for phases which
4 * employ excess Gibbs free energy formulations related to Margules
5 * expansions (see @ref thermoprops
6 * and class @link Cantera::MargulesVPSSTP MargulesVPSSTP@endlink).
7 */
8
9// This file is part of Cantera. See License.txt in the top-level directory or
10// at https://cantera.org/license.txt for license and copyright information.
11
15
16namespace Cantera
17{
18MargulesVPSSTP::MargulesVPSSTP(const string& inputFile, const string& id_)
19{
20 initThermoFile(inputFile, id_);
21}
22
23// -- Activities, Standard States, Activity Concentrations -----------
24
26{
27 // Update the activity coefficients
29
30 // take the exp of the internally stored coefficients.
31 for (size_t k = 0; k < m_kk; k++) {
32 lnac[k] = lnActCoeff_Scaled_[k];
33 }
34}
35
36// ------------ Partial Molar Properties of the Solution ------------
37
39{
40 // First get the standard chemical potentials in molar form. This requires
41 // updates of standard state as a function of T and P
43
44 // Update the activity coefficients
46 for (size_t k = 0; k < m_kk; k++) {
47 double xx = std::max(moleFractions_[k], SmallNumber);
48 mu[k] += RT() * (log(xx) + lnActCoeff_Scaled_[k]);
49 }
50}
51
53{
54 size_t kk = nSpecies();
55 double h = 0;
56 vector<double> hbar(kk);
58 for (size_t i = 0; i < kk; i++) {
59 h += moleFractions_[i]*hbar[i];
60 }
61 return h;
62}
63
65{
66 size_t kk = nSpecies();
67 double s = 0;
68 vector<double> sbar(kk);
70 for (size_t i = 0; i < kk; i++) {
71 s += moleFractions_[i]*sbar[i];
72 }
73 return s;
74}
75
77{
78 size_t kk = nSpecies();
79 double cp = 0;
80 vector<double> cpbar(kk);
81 getPartialMolarCp(&cpbar[0]);
82 for (size_t i = 0; i < kk; i++) {
83 cp += moleFractions_[i]*cpbar[i];
84 }
85 return cp;
86}
87
89{
90 return cp_mole() - GasConstant;
91}
92
94{
95 // Get the nondimensional standard state enthalpies
96 getEnthalpy_RT(hbar);
97
98 // dimensionalize it.
99 for (size_t k = 0; k < m_kk; k++) {
100 hbar[k] *= RT();
101 }
102
103 // Update the activity coefficients, This also update the internally stored
104 // molalities.
107 for (size_t k = 0; k < m_kk; k++) {
108 hbar[k] -= RT() * temperature() * dlnActCoeffdT_Scaled_[k];
109 }
110}
111
112void MargulesVPSSTP::getPartialMolarCp(double* cpbar) const
113{
114 // Get the nondimensional standard state entropies
115 getCp_R(cpbar);
116 double T = temperature();
117
118 // Update the activity coefficients, This also update the internally stored
119 // molalities.
122
123 for (size_t k = 0; k < m_kk; k++) {
124 cpbar[k] -= 2 * T * dlnActCoeffdT_Scaled_[k] + T * T * d2lnActCoeffdT2_Scaled_[k];
125 }
126 // dimensionalize it.
127 for (size_t k = 0; k < m_kk; k++) {
128 cpbar[k] *= GasConstant;
129 }
130}
131
133{
134 // Get the nondimensional standard state entropies
135 getEntropy_R(sbar);
136 double T = temperature();
137
138 // Update the activity coefficients, This also update the internally stored
139 // molalities.
142
143 for (size_t k = 0; k < m_kk; k++) {
144 double xx = std::max(moleFractions_[k], SmallNumber);
145 sbar[k] += - lnActCoeff_Scaled_[k] -log(xx) - T * dlnActCoeffdT_Scaled_[k];
146 }
147
148 // dimensionalize it.
149 for (size_t k = 0; k < m_kk; k++) {
150 sbar[k] *= GasConstant;
151 }
152}
153
155{
156 double T = temperature();
157
158 // Get the standard state values in m^3 kmol-1
159 getStandardVolumes(vbar);
160
161 for (size_t i = 0; i < numBinaryInteractions_; i++) {
162 size_t iA = m_pSpecies_A_ij[i];
163 size_t iB = m_pSpecies_B_ij[i];
164 double XA = moleFractions_[iA];
165 double XB = moleFractions_[iB];
166 double g0 = (m_VHE_b_ij[i] - T * m_VSE_b_ij[i]);
167 double g1 = (m_VHE_c_ij[i] - T * m_VSE_c_ij[i]);
168 const double temp1 = g0 + g1 * XB;
169 const double all = -1.0*XA*XB*temp1 - XA*XB*XB*g1;
170
171 for (size_t iK = 0; iK < m_kk; iK++) {
172 vbar[iK] += all;
173 }
174 vbar[iA] += XB * temp1;
175 vbar[iB] += XA * temp1 + XA*XB*g1;
176 }
177}
178
180{
181 initLengths();
182 if (m_input.hasKey("interactions")) {
183 for (auto& item : m_input["interactions"].asVector<AnyMap>()) {
184 auto& species = item["species"].asVector<string>(2);
185 vector<double> h(2), s(2), vh(2), vs(2);
186 if (item.hasKey("excess-enthalpy")) {
187 h = item.convertVector("excess-enthalpy", "J/kmol", 2);
188 }
189 if (item.hasKey("excess-entropy")) {
190 s = item.convertVector("excess-entropy", "J/kmol/K", 2);
191 }
192 if (item.hasKey("excess-volume-enthalpy")) {
193 vh = item.convertVector("excess-volume-enthalpy", "m^3/kmol", 2);
194 }
195 if (item.hasKey("excess-volume-entropy")) {
196 vs = item.convertVector("excess-volume-entropy", "m^3/kmol/K", 2);
197 }
199 h[0], h[1], s[0], s[1], vh[0], vh[1], vs[0], vs[1]);
200 }
201 }
203}
204
206{
208 vector<AnyMap> interactions;
209 for (size_t n = 0; n < m_pSpecies_A_ij.size(); n++) {
210 AnyMap interaction;
211 interaction["species"] = vector<string>{
213 if (m_HE_b_ij[n] != 0 || m_HE_c_ij[n] != 0) {
214 interaction["excess-enthalpy"].setQuantity(
215 {m_HE_b_ij[n], m_HE_c_ij[n]}, "J/kmol");
216 }
217 if (m_SE_b_ij[n] != 0 || m_SE_c_ij[n] != 0) {
218 interaction["excess-entropy"].setQuantity(
219 {m_SE_b_ij[n], m_SE_c_ij[n]}, "J/kmol/K");
220 }
221 if (m_VHE_b_ij[n] != 0 || m_VHE_c_ij[n] != 0) {
222 interaction["excess-volume-enthalpy"].setQuantity(
223 {m_VHE_b_ij[n], m_VHE_c_ij[n]}, "m^3/kmol");
224 }
225 if (m_VSE_b_ij[n] != 0 || m_VSE_c_ij[n] != 0) {
226 interaction["excess-volume-entropy"].setQuantity(
227 {m_VSE_b_ij[n], m_VSE_c_ij[n]}, "m^3/kmol/K");
228 }
229 interactions.push_back(std::move(interaction));
230 }
231 phaseNode["interactions"] = std::move(interactions);
232}
233
235{
237}
238
239void MargulesVPSSTP::addBinaryInteraction(const string& speciesA,
240 const string& speciesB, double h0, double h1, double s0, double s1,
241 double vh0, double vh1, double vs0, double vs1)
242{
243 size_t kA = speciesIndex(speciesA);
244 size_t kB = speciesIndex(speciesB);
245 // The interaction is silently ignored if either species is not defined in
246 // the current phase.
247 if (kA == npos || kB == npos) {
248 return;
249 }
250 m_pSpecies_A_ij.push_back(kA);
251 m_pSpecies_B_ij.push_back(kB);
252
253 m_HE_b_ij.push_back(h0);
254 m_HE_c_ij.push_back(h1);
255 m_SE_b_ij.push_back(s0);
256 m_SE_c_ij.push_back(s1);
257 m_VHE_b_ij.push_back(vh0);
258 m_VHE_c_ij.push_back(vh1);
259 m_VSE_b_ij.push_back(vs0);
260 m_VSE_c_ij.push_back(vs1);
262}
263
264
266{
267 double T = temperature();
268 lnActCoeff_Scaled_.assign(m_kk, 0.0);
269 for (size_t i = 0; i < numBinaryInteractions_; i++) {
270 size_t iA = m_pSpecies_A_ij[i];
271 size_t iB = m_pSpecies_B_ij[i];
272 double g0 = (m_HE_b_ij[i] - T * m_SE_b_ij[i]) / RT();
273 double g1 = (m_HE_c_ij[i] - T * m_SE_c_ij[i]) / RT();
274 double XA = moleFractions_[iA];
275 double XB = moleFractions_[iB];
276 const double XAXB = XA * XB;
277 const double g0g1XB = (g0 + g1 * XB);
278 const double all = -1.0 * XAXB * g0g1XB - XAXB * XB * g1;
279 for (size_t iK = 0; iK < m_kk; iK++) {
280 lnActCoeff_Scaled_[iK] += all;
281 }
282 lnActCoeff_Scaled_[iA] += XB * g0g1XB;
283 lnActCoeff_Scaled_[iB] += XA * g0g1XB + XAXB * g1;
284 }
285}
286
288{
289 double invT = 1.0 / temperature();
290 double invRTT = 1.0 / GasConstant*invT*invT;
291 dlnActCoeffdT_Scaled_.assign(m_kk, 0.0);
292 d2lnActCoeffdT2_Scaled_.assign(m_kk, 0.0);
293 for (size_t i = 0; i < numBinaryInteractions_; i++) {
294 size_t iA = m_pSpecies_A_ij[i];
295 size_t iB = m_pSpecies_B_ij[i];
296 double XA = moleFractions_[iA];
297 double XB = moleFractions_[iB];
298 double g0 = -m_HE_b_ij[i] * invRTT;
299 double g1 = -m_HE_c_ij[i] * invRTT;
300 const double XAXB = XA * XB;
301 const double g0g1XB = (g0 + g1 * XB);
302 const double all = -1.0 * XAXB * g0g1XB - XAXB * XB * g1;
303 const double mult = 2.0 * invT;
304 const double dT2all = mult * all;
305 for (size_t iK = 0; iK < m_kk; iK++) {
306 dlnActCoeffdT_Scaled_[iK] += all;
307 d2lnActCoeffdT2_Scaled_[iK] -= dT2all;
308 }
309 dlnActCoeffdT_Scaled_[iA] += XB * g0g1XB;
310 dlnActCoeffdT_Scaled_[iB] += XA * g0g1XB + XAXB * g1;
311 d2lnActCoeffdT2_Scaled_[iA] -= mult * XB * g0g1XB;
312 d2lnActCoeffdT2_Scaled_[iB] -= mult * (XA * g0g1XB + XAXB * g1);
313 }
314}
315
316void MargulesVPSSTP::getdlnActCoeffdT(double* dlnActCoeffdT) const
317{
319 for (size_t k = 0; k < m_kk; k++) {
320 dlnActCoeffdT[k] = dlnActCoeffdT_Scaled_[k];
321 }
322}
323
324void MargulesVPSSTP::getd2lnActCoeffdT2(double* d2lnActCoeffdT2) const
325{
327 for (size_t k = 0; k < m_kk; k++) {
328 d2lnActCoeffdT2[k] = d2lnActCoeffdT2_Scaled_[k];
329 }
330}
331
332void MargulesVPSSTP::getdlnActCoeffds(const double dTds, const double* const dXds,
333 double* dlnActCoeffds) const
334{
335 double T = temperature();
337 for (size_t iK = 0; iK < m_kk; iK++) {
338 dlnActCoeffds[iK] = 0.0;
339 }
340
341 for (size_t i = 0; i < numBinaryInteractions_; i++) {
342 size_t iA = m_pSpecies_A_ij[i];
343 size_t iB = m_pSpecies_B_ij[i];
344 double XA = moleFractions_[iA];
345 double XB = moleFractions_[iB];
346 double dXA = dXds[iA];
347 double dXB = dXds[iB];
348 double g0 = (m_HE_b_ij[i] - T * m_SE_b_ij[i]) / RT();
349 double g1 = (m_HE_c_ij[i] - T * m_SE_c_ij[i]) / RT();
350 const double g02g1XB = g0 + 2*g1*XB;
351 const double g2XAdXB = 2*g1*XA*dXB;
352 const double all = (-XB * dXA - XA *dXB) * g02g1XB - XB *g2XAdXB;
353 for (size_t iK = 0; iK < m_kk; iK++) {
354 dlnActCoeffds[iK] += all + dlnActCoeffdT_Scaled_[iK]*dTds;
355 }
356 dlnActCoeffds[iA] += dXB * g02g1XB;
357 dlnActCoeffds[iB] += dXA * g02g1XB + g2XAdXB;
358 }
359}
360
362{
363 double T = temperature();
364 dlnActCoeffdlnN_diag_.assign(m_kk, 0.0);
365
366 for (size_t iK = 0; iK < m_kk; iK++) {
367 double XK = moleFractions_[iK];
368
369 for (size_t i = 0; i < numBinaryInteractions_; i++) {
370 size_t iA = m_pSpecies_A_ij[i];
371 size_t iB = m_pSpecies_B_ij[i];
372 size_t delAK = 0;
373 size_t delBK = 0;
374
375 if (iA==iK) {
376 delAK = 1;
377 } else if (iB==iK) {
378 delBK = 1;
379 }
380
381 double XA = moleFractions_[iA];
382 double XB = moleFractions_[iB];
383
384 double g0 = (m_HE_b_ij[i] - T * m_SE_b_ij[i]) / RT();
385 double g1 = (m_HE_c_ij[i] - T * m_SE_c_ij[i]) / RT();
386
387 dlnActCoeffdlnN_diag_[iK] += 2*(delBK-XB)*(g0*(delAK-XA)+g1*(2*(delAK-XA)*XB+XA*(delBK-XB)));
388 }
390 }
391}
392
394{
395 double T = temperature();
397
398 // Loop over the activity coefficient gamma_k
399 for (size_t iK = 0; iK < m_kk; iK++) {
400 for (size_t iM = 0; iM < m_kk; iM++) {
401 double XM = moleFractions_[iM];
402 for (size_t i = 0; i < numBinaryInteractions_; i++) {
403 size_t iA = m_pSpecies_A_ij[i];
404 size_t iB = m_pSpecies_B_ij[i];
405 double delAK = 0.0;
406 double delBK = 0.0;
407 double delAM = 0.0;
408 double delBM = 0.0;
409 if (iA==iK) {
410 delAK = 1.0;
411 } else if (iB==iK) {
412 delBK = 1.0;
413 }
414 if (iA==iM) {
415 delAM = 1.0;
416 } else if (iB==iM) {
417 delBM = 1.0;
418 }
419
420 double XA = moleFractions_[iA];
421 double XB = moleFractions_[iB];
422 double g0 = (m_HE_b_ij[i] - T * m_SE_b_ij[i]) / RT();
423 double g1 = (m_HE_c_ij[i] - T * m_SE_c_ij[i]) / RT();
424 dlnActCoeffdlnN_(iK,iM) += g0*((delAM-XA)*(delBK-XB)+(delAK-XA)*(delBM-XB));
425 dlnActCoeffdlnN_(iK,iM) += 2*g1*((delAM-XA)*(delBK-XB)*XB+(delAK-XA)*(delBM-XB)*XB+(delBM-XB)*(delBK-XB)*XA);
426 }
427 dlnActCoeffdlnN_(iK,iM) = XM*dlnActCoeffdlnN_(iK,iM);
428 }
429 }
430}
431
433{
434 double T = temperature();
435 dlnActCoeffdlnX_diag_.assign(m_kk, 0.0);
436
437 for (size_t i = 0; i < numBinaryInteractions_; i++) {
438 size_t iA = m_pSpecies_A_ij[i];
439 size_t iB = m_pSpecies_B_ij[i];
440
441 double XA = moleFractions_[iA];
442 double XB = moleFractions_[iB];
443
444 double g0 = (m_HE_b_ij[i] - T * m_SE_b_ij[i]) / RT();
445 double g1 = (m_HE_c_ij[i] - T * m_SE_c_ij[i]) / RT();
446
447 dlnActCoeffdlnX_diag_[iA] += XA*XB*(2*g1*-2*g0-6*g1*XB);
448 dlnActCoeffdlnX_diag_[iB] += XA*XB*(2*g1*-2*g0-6*g1*XB);
449 }
450}
451
452void MargulesVPSSTP::getdlnActCoeffdlnN_diag(double* dlnActCoeffdlnN_diag) const
453{
455 for (size_t k = 0; k < m_kk; k++) {
456 dlnActCoeffdlnN_diag[k] = dlnActCoeffdlnN_diag_[k];
457 }
458}
459
460void MargulesVPSSTP::getdlnActCoeffdlnX_diag(double* dlnActCoeffdlnX_diag) const
461{
463 for (size_t k = 0; k < m_kk; k++) {
464 dlnActCoeffdlnX_diag[k] = dlnActCoeffdlnX_diag_[k];
465 }
466}
467
468void MargulesVPSSTP::getdlnActCoeffdlnN(const size_t ld, double* dlnActCoeffdlnN)
469{
471 double* data = & dlnActCoeffdlnN_(0,0);
472 for (size_t k = 0; k < m_kk; k++) {
473 for (size_t m = 0; m < m_kk; m++) {
474 dlnActCoeffdlnN[ld * k + m] = data[m_kk * k + m];
475 }
476 }
477}
478
479}
(see Thermodynamic Properties and class MargulesVPSSTP).
Headers for the factory class that can create known ThermoPhase objects (see Thermodynamic Properties...
A map of string keys to values whose type can vary at runtime.
Definition AnyMap.h:427
bool hasKey(const string &key) const
Returns true if the map contains an item named key.
Definition AnyMap.cpp:1423
void zero()
Set all of the entries to zero.
Definition Array.h:127
virtual void resize(size_t n, size_t m, double v=0.0)
Resize the array, and fill the new entries with 'v'.
Definition Array.cpp:47
vector< double > d2lnActCoeffdT2_Scaled_
Storage for the current derivative values of the gradients with respect to temperature of the log of ...
Array2D dlnActCoeffdlnN_
Storage for the current derivative values of the gradients with respect to logarithm of the species m...
vector< double > lnActCoeff_Scaled_
Storage for the current values of the activity coefficients of the species.
vector< double > dlnActCoeffdlnX_diag_
Storage for the current derivative values of the gradients with respect to logarithm of the mole frac...
vector< double > moleFractions_
Storage for the current values of the mole fractions of the species.
vector< double > dlnActCoeffdT_Scaled_
Storage for the current derivative values of the gradients with respect to temperature of the log of ...
vector< double > dlnActCoeffdlnN_diag_
Storage for the current derivative values of the gradients with respect to logarithm of the mole frac...
void getdlnActCoeffds(const double dTds, const double *const dXds, double *dlnActCoeffds) const override
Get the change in activity coefficients wrt changes in state (temp, mole fraction,...
double enthalpy_mole() const override
Molar enthalpy. Units: J/kmol.
void getPartialMolarEnthalpies(double *hbar) const override
Returns an array of partial molar enthalpies for the species in the mixture.
void getChemPotentials(double *mu) const override
Get the species chemical potentials. Units: J/kmol.
vector< double > m_VHE_c_ij
Enthalpy term for the ternary mole fraction interaction of the excess Gibbs free energy expression.
vector< double > m_SE_b_ij
Entropy term for the binary mole fraction interaction of the excess Gibbs free energy expression.
size_t numBinaryInteractions_
number of binary interaction expressions
vector< double > m_SE_c_ij
Entropy term for the ternary mole fraction interaction of the excess Gibbs free energy expression.
void s_update_dlnActCoeff_dlnN_diag() const
Update the derivative of the log of the activity coefficients wrt log(moles) - diagonal only.
void getParameters(AnyMap &phaseNode) const override
Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using ...
void initThermo() override
Initialize the ThermoPhase object after all species have been set up.
void getPartialMolarVolumes(double *vbar) const override
Return an array of partial molar volumes for the species in the mixture.
vector< size_t > m_pSpecies_A_ij
vector of species indices representing species A in the interaction
double cv_mole() const override
Molar heat capacity at constant volume. Units: J/kmol/K.
void s_update_dlnActCoeff_dT() const
Update the derivative of the log of the activity coefficients wrt T.
vector< size_t > m_pSpecies_B_ij
vector of species indices representing species B in the interaction
vector< double > m_VSE_c_ij
Entropy term for the ternary mole fraction interaction of the excess Gibbs free energy expression.
void s_update_dlnActCoeff_dlnN() const
Update the derivative of the log of the activity coefficients wrt log(moles_m)
double entropy_mole() const override
Molar entropy. Units: J/kmol/K.
vector< double > m_HE_b_ij
Enthalpy term for the binary mole fraction interaction of the excess Gibbs free energy expression.
void getdlnActCoeffdT(double *dlnActCoeffdT) const override
Get the array of temperature derivatives of the log activity coefficients.
vector< double > m_VSE_b_ij
Entropy term for the binary mole fraction interaction of the excess Gibbs free energy expression.
double cp_mole() const override
Molar heat capacity at constant pressure. Units: J/kmol/K.
void getPartialMolarCp(double *cpbar) const override
Returns an array of partial molar entropies for the species in the mixture.
void initLengths()
Initialize lengths of local variables after all species have been identified.
void getLnActivityCoefficients(double *lnac) const override
Get the array of non-dimensional molar-based ln activity coefficients at the current solution tempera...
void s_update_dlnActCoeff_dlnX_diag() const
Update the derivative of the log of the activity coefficients wrt log(mole fraction)
void s_update_lnActCoeff() const
Update the activity coefficients.
void getdlnActCoeffdlnX_diag(double *dlnActCoeffdlnX_diag) const override
Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component o...
vector< double > m_VHE_b_ij
Enthalpy term for the binary mole fraction interaction of the excess Gibbs free energy expression.
void addBinaryInteraction(const string &speciesA, const string &speciesB, double h0, double h1, double s0, double s1, double vh0, double vh1, double vs0, double vs1)
Add a binary species interaction with the specified parameters.
MargulesVPSSTP(const string &inputFile="", const string &id="")
Construct a MargulesVPSSTP object from an input file.
vector< double > m_HE_c_ij
Enthalpy term for the ternary mole fraction interaction of the excess Gibbs free energy expression.
void getdlnActCoeffdlnN_diag(double *dlnActCoeffdlnN_diag) const override
Get the array of log species mole number derivatives of the log activity coefficients.
void getd2lnActCoeffdT2(double *d2lnActCoeffdT2) const
Get the array of temperature second derivatives of the log activity coefficients.
void getPartialMolarEntropies(double *sbar) const override
Returns an array of partial molar entropies for the species in the mixture.
void getdlnActCoeffdlnN(const size_t ld, double *const dlnActCoeffdlnN) override
Get the array of derivatives of the log activity coefficients with respect to the log of the species ...
size_t nSpecies() const
Returns the number of species in the phase.
Definition Phase.h:231
size_t m_kk
Number of species in the phase.
Definition Phase.h:842
double temperature() const
Temperature (K).
Definition Phase.h:562
string speciesName(size_t k) const
Name of the species with index k.
Definition Phase.cpp:142
size_t speciesIndex(const string &name) const
Returns the index of a species named 'name' within the Phase object.
Definition Phase.cpp:129
shared_ptr< Species > species(const string &name) const
Return the Species object for the named species.
Definition Phase.cpp:856
virtual void getParameters(AnyMap &phaseNode) const
Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using ...
double RT() const
Return the Gas Constant multiplied by the current temperature.
virtual void initThermo()
Initialize the ThermoPhase object after all species have been set up.
void initThermoFile(const string &inputFile, const string &id)
Initialize a ThermoPhase object using an input file.
AnyMap m_input
Data supplied via setParameters.
void getEntropy_R(double *sr) const override
Get the array of nondimensional Entropy functions for the standard state species at the current T and...
void getStandardChemPotentials(double *mu) const override
Get the array of chemical potentials at unit activity for the species at their standard states at the...
void getCp_R(double *cpr) const override
Get the nondimensional Heat Capacities at constant pressure for the species standard states at the cu...
void getEnthalpy_RT(double *hrt) const override
Get the nondimensional Enthalpy functions for the species at their standard states at the current T a...
void getStandardVolumes(double *vol) const override
Get the molar volumes of the species standard states at the current T and P of the solution.
const double GasConstant
Universal Gas Constant [J/kmol/K].
Definition ct_defs.h:120
Namespace for the Cantera kernel.
Definition AnyMap.cpp:564
const size_t npos
index returned by functions to indicate "no position"
Definition ct_defs.h:180
const double SmallNumber
smallest number to compare to zero.
Definition ct_defs.h:158
Contains declarations for string manipulation functions within Cantera.