(adsbygoogle = window.adsbygoogle || []).push({}); 1. A friend suggests to you an alternative to the Virial equation of state: P=(RT/V_{m})-(B/V_{m}^{2})+(C/V_{m}^{3})

a.) Show that this equation is useful by proving that it demonstrates critical behavior.

b.) Find the critical constants P_{c}, V_{m,c}, and T_{c}in terms of B, C and R.

c.) Calculate the compressibility factor Z_{c}.

Vm=molar volume, P=pressure, T=temp, and B&C would normally be the first and second virial constants.

2. I know that first and second derivatives of pressure with respect to volume should be zero at the critical temperature.

3. Through an algebraic nightmare, I figured out that T_{c}is equal to (6Vm^3(B+C)-12C+2BVm^2)/(RVm^2(2+Vm)) by taking the first and second derivatives, then setting them equal to each other since they should both be zero at Tc. I have no idea how to find Pc, Vc or Vm since it doesn't appear possible to isolate Vm. How should I proceed?

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# Alternative Real Gas Equation of State

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