Question

At critical temperature,pressure and volume,the compressibility factors (Z),is?

Answer 1

When you calculate the critical constant using Vanderwaal equation by taking l.c.m,then you will find a cubic equation means having 3 roots.and at critical point all three roots will be equal therefore the equation will be like

Vm^3–(b+RTc/Pc)Vm^2+(a/Pc)Vm-ab/Pc=0(equation 1)

Where Vm=Vc due to equal roots

Therefore according to equal root condition

(Vm-Vc) (Vm-Vc) (Vm-Vc)=0 i.e. equal to

Vm^3-3VcVm^2+3Vc^2Vm-Vc^3=0(equation 2)

Compare both equation 1 and 2 you will get

b+RTc/Pc=3Vc, a/Pc=3Vc^2, ab/Pc=Vc^3

Then Tc=8a/27bR, Pc=a/27b^2, Vc=3b

Since Z=PcVc/RTc at critical point therefore by putting the value of Tc,Vc,Pc you will get3/8 or(.375)always.

Therefore answer will be 3/8

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