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Defining a thermodynamic system completely

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So I read somewhere that if we know u(s,v) i.e. internal energy as a function of entropy and specific volume, we can find all other thermodynamics quantities on earth, like temperature, pressure, Gibb's free energy from it.

However, is this true if we have u as a function of just any two thermodynamic properties?

Also. if we know Gibb's free energy/ Helmoltz energy in terms of any 2 quantities, can we similarly find all other thermodynamic properties from it? In case there is a chemical reaction going on, then I guess we need to define 2 such parameters, right?

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