?Find expressions for \(\hat{\phi}_{1} \text { and } \hat{\phi}_{2}\) for a binary gas

Chapter 13, Problem 13.66

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Find expressions for \(\hat{\phi}_{1} \text { and } \hat{\phi}_{2}\) for a binary gas mixture described by Eq. (3.38). The mixing rule for B is given by Eq. (10.62). The mixing rule for C is given by the general equation:

\(C=\sum_{i} \sum_{j} \sum_{k} y_{i} y_{j} y_{k} C_{i j k}\)

where Cs with the same subscripts, regardless of order, are equal. For a binary mixture, this becomes:

\(C=y_{1}^{3} C_{111}+3 y_{1}^{2} y_{2} C_{112}+3 y_{1} y_{2}^{2} C_{122}+y_{2}^{3} C_{222}\)

Text Transcription:

hat phi_1 and hat phi_2

C=sum_i sum_j sum_k y_i y_j y_k C_ijk

C=y_1^3 C_111+3 y_1^2 y_2 C_112+3y_1 y_2^2 C_122+y_2^3 C_222

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