# How can internal energy be expressed as a function of any two of $p, v, T$?

In the book of Irey, Theormodynamics, the author states that (while talking about single phase substances)

For a simple compressible media, we may choose our measurable independent variables any two of $$p, v, T$$.The traditional choice for internal energy is temperature and specific volume, $$u = u(T,v)$$.

However, this statement is as if it just falls from the sky; he does not provide any argument why $$u$$ can be expressed as a function of any two of those variable, nor does he give any argument about the relationship of one of those variables to another two.

Question:

I'm looking for an explanation about the concerns that I raised above.

Edit:

As @SolarMike pointed out, the author explicitly consider gaseous substances in the above comment; however, later he also defines $$Z = \frac{ pv}{RT } = Z (p, T) ,$$ i.e knowing $$p,T$$ allows you to calculate $$Z$$, and then you can find $$v$$, but he still does not give any argument why $$Z = Z (p,T)$$. As far as I can see, Charles's law, and the other two law accompanying it are for ideal gases, but we are not woking with ideal gases, yet.

• Just like Ohm's law, knowing two defines the third... – user207455 Jun 3 at 12:47
• @SolarMike I got it, but why and how ? what is that relationship, i.e if I give any two of them what is the third one in terms of the first two ? – onurcanbektas Jun 3 at 12:49
• So what relates p, v & T - have you looked at Boyles or Charles laws and the universal gas constant? – user207455 Jun 3 at 12:52
• @SolarMike The author talks about a single phase substances in general, not just gases. As far as I know, those law valid only for gases. – onurcanbektas Jun 3 at 12:55
• Is not the statement "compressible media" - I'm assuming "compressile" was your typing... – user207455 Jun 3 at 12:57