a) Determine whether the van der Waals equation of state admits a critical point

Question

a) Determine whether the van der Waals equation of state admits a critical point. If so, at what volume, pressure and temperature? Leave in terms of a and b. (if no, put NA in Blanks 2-4) (for powers, use ^)

Blank #1: yes or no

Blank #2: Vc

Blank #3: Pc

Blank #4: Tc

b) Say the equation of state had no attractive part, just an excluded volume: p=(nRT)/(V?nB)

Does the equation have a critical point?

Blank #5: yes or no

Please show the work and explain.

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Explanation / Answer

1) yes

2) Vc = 3b

3) Pc = a / 27 b2

4) Tc = 8a / 27 bR

5) no

explanation:

these are derived from vanderwalls equation and critical point equation.

these are all direct formulas interms of a, b.

by solving and comparing valuesof both vandewall and critical equation we get all values

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