?Analogous to the conventional partial property \(\bar{M}_{i}\), one can define a

Chapter 10, Problem 10.15

(choose chapter or problem)

Analogous to the conventional partial property \(\bar{M}_{i}\), one can define a constant-T, V partial property \(\tilde{M}_{i}\):

\(\tilde{M}_{i} \equiv\left[\frac{\partial(n M)}{\partial n_{i}}\right]_{T, V, n_{j}}\)

Show that \(\tilde{M}_{i} \text { and } \bar{M}_{i}\) are related by the equation:

\(\tilde{M}_{i}=\bar{M}_{i}+\left(V-\bar{V}_{i}\right)\left(\frac{\partial M}{\partial V}\right)_{T, x}\)

Demonstrate that the \(\tilde{M}_{i}\) satisfies a summability relation, \(M=\sum_{i} x_{i} \tilde{M}_{i}\).

Text Transcription:

barM_i

tildeM_i

tildeM_i equiv [partial(nM)/partial n_i]_T, V, n_j

tildeM_i and barM_i

tildeM_i = barM_i + (V - barV_i) (partial M/partial V)_T,x

M=sum_i x_i tildeM_i