Chapter 10, Problem 10.15P

Interpretation Introduction

Interpretation:

To show that,

  $\widetilde{M_i}=\overline{M_i}+(V-V_i){\left(\frac{\partial M}{\partial V}\right)}_{T,n}$

And if $\widetilde{M_i}$ satisfies the summability relation $M={\displaystyle \sum _i{x}_i\widetilde{M_i}}$

Concept Introduction :

The conventional partial property with constant T, P is defined as,

  $\overline{M_i}={\left[\frac{\partial (nM)}{\partial n_i}\right]}_{T,P,n_j}$

The conventional partial property with constant T, V is defined as,

  $\widetilde{M_i}={\left[\frac{\partial (nM)}{\partial n_i}\right]}_{T,V,n_j}$

Where,

T = Temperature

V = Volume

P = Pressure

n = total number of moles

n_i = Number of moles of species

n_j = Number of moles of species taken constant

V_i = Individual volumes of species

x_i = Mole fraction of individual species