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I came across a question that inquired about whether there exists any intensive property of a system, that is independent of temperature and then seeks proof for the presence/absence of such properties, from a quasi-theoretical standpoint. The question mentions that the system shall be assumed to be non-ideal (ideal gas laws don't hold true et al).

How to proceed, for the latter? Does there exist any such property, in the first place?

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  • $\begingroup$ Make a list of intensive properties from here en.wikipedia.org/wiki/…, I can think of concentration as one example. $\endgroup$ – M. Farooq Nov 29 '19 at 16:11
  • $\begingroup$ Concentration depends on temperature via temperature dependent density. $\endgroup$ – Poutnik Nov 29 '19 at 18:12
  • $\begingroup$ @Poutnik, yes but what does density have to do with concentration? If we have 1 M NaCl in a closed container in water, what will temperature do to concentration, as long as there is no phase change? $\endgroup$ – M. Farooq Nov 30 '19 at 2:37
  • $\begingroup$ Liquid thermal dilation decreases concentration. $\endgroup$ – Poutnik Nov 30 '19 at 2:51
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    $\begingroup$ @M. Farooq If you heat up 1 M NaCl to 100 deg C, the concentration will be several percent lower, as the volume will be several percent bigger. It affects also accurate preparation of titration stock solution and volumetry vessel volume calibration. $\endgroup$ – Poutnik Dec 2 '19 at 15:17
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After looking at the list in the Wikipedia article linked in the comment by M.Farooq, I suspect there are few properties that are guaranteed to be independent of temperature, an exception being molality and mole fraction in a closed system and absence of reactions. Other concentrations that are functions of volume are bound to be functions of temperature. Even in the presence of reactions, the atomic mole fraction is bound to be a constant (absent nuclear reactions, that is).

Standard molar quantities and some other properties are defined at fixed temperatures and are therefore strictly temperature independent, but that makes for a circular argument, and presumably this is not the type of property the question is about.

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The atomic/molecular/formula weight (choose whichever is appropriate) of a substance is an intensive property (it is inherent to the substance itself, and is independent of how much of the substance you have), and is independent of temperature (if you raise the temperature high enough to cause a chemical or nuclear reaction, it's no longer that substance).

If you wanted to apply this to a system, it's straightforward if the system consists of only a pure substance. Otherwise you could say that, if the system is closed, in the absence of chemical and nuclear reactions, the average atomic/molecular/formula weight is independent of temperature.

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