Equilibrium and entropy - Classical thermodynamics

5 important questions on Equilibrium and entropy - Classical thermodynamics

What mathematical properties do all entropy function have in common?

1. Partial derivatives
2. Extensivity
3. Concavity

Of the properties that are the same for all entropy functions, what are the partial derivatives?

Where T is the absolute temperature, P the absolute pressure and μ the chemical potential.

Of the properties that are the same for all entropy functions, what is the extensivity?

λ can be any real positive number.
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Of the properties that are the same for all entropy functions, what is the concavity?

X, Y, Z are E, V, N in any order

How much information is needed to specify the equilibrium state?

For a single component system three variables need to be known to specify the equilibrium state of the system.
For multi component systems #component + 2 variables are needed.

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