The van der Waals' equation of law of corresponding states for 1 mole of gas is :

Options

A. `(P_(r)+(3)/(V_(r)^(2)))(3V_(r)-1)=8T_(r)`
B. `(P_(r)-(3)/(V_(r)^(2)))(3V_(r)-1)=8T_(r)`
C. `(P_(r)+(3)/(V_(r)^(2)))(3V_(r)+1)=8piT_(r)`
D. `(P_(r)+(3)/(V_(r)^(2)))(3V_(r)+1)=8`

Answer

a

Explanation

(a) The van der Waals' equation for 1 mole of gas is
`(P+(a)/(V^(2)))(V-b)=RT`
if we put, `P_(r)=(P)/(P_(C)),V_(r)=(V_(m))/(V_(C))` and `T_(r)=(T)/(T_(C)),`
`( :' P_(C)=(a)/(27b^(2)),V_(C) =3b and T_(C)=(8a)/(27Rb))`
`(P_(r)((a^(2))/(27b^(2)))+(a)/(V_(r)^(2)(3b)^(2)))(V_(r)(3b)-b)=RT_(r)((8a)/(27Rb))`
This equation is called van der Waals' equation of law of corresponding states.