Question

Show that under conditions of low pressure (and hence low densities), the Dieterici
equation of state reduces to the van der Waals equation of state,​

Answer 1

Answer:

At low pressure, the van der Waals' equation is reduced to

Z=  P$V_{m}$/RT  = 1 − a/ RT$V_{m}$

The van der Waals' equation is

(P+  a/$V_{m} ^{2}$) ($V_{m}$ - b) = Rt

At low pressure, volume is very giant and also  the correction term b (a constant of tiny value) are often neglected in comparision to very giant value of the volume.

(P+  a/$V_{m} ^{2}$) ($V_{m}$) = RT​    

P$V_{m}$ = a/$V_{m}$ = RT

P$V_{m}$ = RT - a/$V_{m}$

​Divide either sides of the equation with RT

P$V_{m}$/RT = 1 - a/RT$V_{m}$

But Z, P$V_{m}$/RT

Hence, P$V_{m}$/RT = 1 - a/RT$V_{m}$