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- Advancement per volume + ('''Advancement per volume''' or volume-spe … '''Advancement per volume''' or volume-specific advancement, d<sub>tr</sub>''Y'', is related to [[advancement]] of a transformation, d<sub>tr</sub>''Y'' = d<sub>tr</sub>''ξ''∙''V''<sup>-1</sup> [MU∙L<sup>-1</sup>]. Compare d<sub>tr</sub>''Y'' with the amount of substance ''j'' per volume, ''c''<sub>''j''</sub> ([[concentration]]), related to [[amount]], ''c''<sub>''j''</sub> = ''n''<sub>''j''</sub>∙''V''<sup>-1</sup> [mol∙''V''<sup>-1</sup>]. Advancement per volume is particularly introduced for chemical reactions, d<sub>r</sub>''Y'', and has the dimension of concentration (amount per volume [mol∙L<sup>-1</sup>]). In an [[open system]] at steady-state, however, the concentration does not change as the reaction advances. Only in [[closed system]]s and [[isolated system]]s, specific advancement equals the change in concentration divided by the stoichiometric number, d<sub>r</sub>''Y'' = d''c''<sub>''j''</sub>/''ν''<sub>''j''</sub> (closed system) d<sub>r</sub>''Y'' = d<sub>r</sub>''c''<sub>''j''</sub>/''ν''<sub>''j''</sub> (general) With a focus on ''internal'' transformations (i; specifically: chemical reactions, r), d''c''<sub>''j''</sub> is replaced by the partial change of concentration, d<sub>r</sub>''c''<sub>''j''</sub> (a transformation variable or process variable). d<sub>r</sub>''c''<sub>''j''</sub> contributes to the total change of concentration, d''c''<sub>''j''</sub> (a system variable or variable of state). In open systems at steady-state, d<sub>r</sub>''c''<sub>''j''</sub> is compensated by ''external processes'', d<sub>e</sub>''c''<sub>''j''</sub> = -d<sub>r</sub>''c''<sub>''j''</sub>, exerting an effect on the total concentration change of substance ''j'', d''c''<sub>''j''</sub> = d<sub>r</sub>''c''<sub>''j''</sub> + d<sub>e</sub>''c''<sub>''j''</sub> = 0 (steady state) d''c''<sub>''j''</sub> = d<sub>r</sub>''c''<sub>''j''</sub> + d<sub>e</sub>''c''<sub>''j''</sub> (general)sses'', d<sub>e</sub>''c''<sub>''j''</sub> = -d<sub>r</sub>''c''<sub>''j''</sub>, exerting an effect on the total concentration change of substance ''j'', d''c''<sub>''j''</sub> = d<sub>r</sub>''c''<sub>''j''</sub> + d<sub>e</sub>''c''<sub>''j''</sub> = 0 (steady state) d''c''<sub>''j''</sub> = d<sub>r</sub>''c''<sub>''j''</sub> + d<sub>e</sub>''c''<sub>''j''</sub> (general))
