Everything about The Van Der Waals Equation totally explained
The
van der Waals equation is an
equation of state for a
fluid composed of particles that have a non-zero size and a pairwise attractive inter-particle
force (such as the
van der Waals force.) It was derived by
Johannes Diderik van der Waals in
1873, based on a modification of the
ideal gas law. The equation approximates the behavior of real fluids, taking into account the nonzero size of molecules and the attraction between them.
Equation
The first form of the van der Waals equation is
» which is unstable; the Van der Waals equation fails to describe real substances in this region. To fix this problem
James Clerk Maxwell (1875) replaces the isotherm between a-c with a horizontal line positioned so that the areas of the two hatched regions are equal. The flat line portion of the isotherm now corresponds to liquid-vapor equilibrium. The portions a-d and c-e are interpreted as metastable states of super-heated liquid and super-cooled vapor respectively.
Maxwell justified the rule by saying that work done on the system in going from c to b should equal work released on going from a to b. (Area on a PV diagram corresponds to mechanical work). That’s because the change in the free energy function A(T,V) equals the work done during a reversible process the free energy function being a state variable should take on a unique value regardless of path. In particular, the value of A at point b should calculate the same regardless of whether the path came from left or right, or went straight across the horizontal isotherm or around the original Van der Waals isotherm.
Maxwell’s argument isn't totally convincing since it requires a reversible path through a region of thermodynamic instability. Nevertheless, more subtle arguments based on modern theories of phase equilibrium seem to confirm the Maxwell Equal Area construction and it remains a valid modification of the Van der Waals equation of state.
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