Advanced Thermodynamics for Engineers, 2nd Edition

PROBLEM

Evaluate the isothermal compressibility, k, and coefficient of expansion, b, of a van der Waals gas.

8.3 LAW OF CORRESPONDING STATES

If it is assumed that all substances obey an equation of the form defined by the van der Waals equation

of state then all state diagrams will be geometrically similar. This means that if the diagrams were

normalised by dividing the properties defining a particular state point (p, v, T) by the properties at the

critical point (p

c

,v

c

,T

c

) then all state diagrams based on these reduced properties will be iden tical.

Thus there would be a general relationship

v

R

¼ f



p

R

; T

R



; (8.16)

where v

R

¼ v=v

c

¼ reduced volume;

p

R

¼ p=