Which of these graphs would be a pure isotherm? A V vs. n graph or a P vs. V graph?

Why is it not the V vs. n graph? It was made at constant temperature, wasn't it?

1 Answer
Truong-Son N.
Jul 26, 2017

It can be, but it is also an isobar, so it is not just at constant temperature, but also constant pressure. It is also a mechanically-open system, i.e. it allows transfer of gas in and out so that n varies, changing the size of the container (e.g. a balloon).

On the other hand, the P-V graph has constant mols of ideal gas and constant temperature, i.e. it follows Boyle's law:

P_1V_1 = P_2V_2, constant n and T

We don't really think about the constant mols of gas in this case, as that can easily be accomplished with a closed system containing a single gas, making this a pure isotherm.

But for the V-n graph, according to Avogadro's principle:

V_1/n_1 = V_2/n_2, constant T and P

So, the V-n graph is not a pure isotherm, but it does involve constant temperature (and pressure). In this case, mols of gas can vary, and thus the system is not mechanically-closed.

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