[G O D I V A]

I dont really understand.  Ive never done Taylor's theorem (wil learn about it at the end of this semester in my maths course) so maybe thats why I dont understand it?

But please, could someone explain it to me?  Here are what my notes say

Virial equation of state and virial coefficients:

   Taylor’s theorem:  For a function f(x) which has n+1 continuous
      derivatives,
      f(x) = f(0) +f(0)’x + [f(0)’’/2!] x2 +…[f(0)(n)/n!] xn…

   Virial equation of state :
      Consider :   Z = f(p)    at a constant T and n
      Apply Taylor theorem to Z = f(p), note that Z -> 1 if p -> 0
            Z = 1 +  B’p + C’ p2 +…
      Or      Vm/Vm0 = pVm/RT = (1 + B’ p + C’ p2 +…)
      Or      p Vm = RT (1 + B’ p + C’ p2 + …)      …..(1)
      Or      p Vm = RT (1 + B/Vm + C /Vm2 + …)  …..(2)
(1)   and (2) are called the virial equation of state. The coefficients (B’, C’…) and (B, C….) are called virial coefficients; they are functions of T and gas molecules.