1.22.2: Volume: Components
One Component
For a system containing one chemical substance we define the volume as follows,
\[\mathrm{V}=\mathrm{V}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}\right] \nonumber \]
The variables in the square brackets are called the INDEPENDENT VARIABLES. The term independent means that within limits, we can change \(\mathrm{T}\) independently of the pressure and \(\mathrm{n}_{1}\); change \(\mathrm{p}\) independently of \(\mathrm{T}\) and \(\mathrm{n}_{1}\); change \(\mathrm{n}_{1}\) independently of \(\mathrm{T}\) and \(\mathrm{p}\). There are some restrictions in our choice of independent variables. At least one of the variables must define the amount of all chemical substances in the system and one variable must define the degree of ‘hotness’ of the system.
Two Chemical Substances
If the composition of a given closed system is specified in terms of the amounts of two chemical substances, 1 and 2, four independent variables \(\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{2}\right]\) define the independent variable \(\mathrm{V}\).
\[\mathrm{V}=\mathrm{V}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{2}\right] \nonumber \]
Volume i - Chemical Substances
For a system containing i - chemical substances where the amounts can be independently varied, the dependent variable \(\mathrm{V}\) is defined by the following equation.
\[\mathrm{V}=\mathrm{V}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{2}, \ldots . \mathrm{n}_{\mathrm{i}}\right] \nonumber \]