Is this the way to calculate the bulk modulus using V. d. Waals-equation?

[tjosan]

Hi,

Is this right?

(p+a(n/v)²)(V-nb)=nRT

Just differentiate both sides with respect to P?

If I do that I get

0=V+P*(dV/dP)_t-nb-(an²)/V²*(dV/dP)_t+2abn³/V³*(dV/dP)_t

(dV/dP)_t=(nb-V) / (P-n²a/V+2an³ab/V³)

And now to calculate the bulk modulus:

k_t=-1/V*(dV/dP)_t = -1/V * (nb-V) / (P-n²a/V+2an³ab/V³)

And one more questions:
What happens to the bulk modulus at the critical point? Is it equal to zero?

 

[Valerie Park]

At the critical point, the bulk modulus tends to infinity as the volume tends to zero. The bulk modulus does not equal zero at the critical point.