Question

why can you write U (Internal energy) as a function of two thermodynamic properties and not all three (P, V, T)? Why is the state fully specified by specifying only two properties? what is the internal energy state equation?

Answer 1

This is based on gibss phase rule.

for example, consider water in a bowl single component . its phase is a liquid phase (single phase).

according to the phase rule number of independent variables required to define a system is given by Gibbs phase rule.

formula F = C - P + 2

F = number of independent variables required to specify any system.

C = number of components

P = number of phases

2 represents any two variables which can be varied (temperature, pressure) or  (temperature, composition) or  (composition, pressure).

for water in bowl F = 1-1+2 = 2

2 independent variables required .

it can be (temperature, pressure) or  (temperature, composition) or  (composition, pressure).

SO now internal energy is a function of (temperature, pressure) or  (temperature, composition) or  (composition, pressure).

We can write U = U(T, P) or U=U(T, V)

If F=3 We require three variables to define system it can be (temperature, pressure, volume) or  (temperature, composition, pressure)

We can write U = U(T, P, V) or U=U(T, V, X)

internal energy state equation is given by the first law of thermodynamics

dQ = dU+dW

TdS = dU + pdV

dU = Tds - PdV