The distribution of the molecular velocities of gas molecules at any temperature `T` is shown below. (The plot below is known as Maxwell's distribution of molecular speeds.)

where
`v` is molecular velocity
`n` is number of molecules having velocity `v`
Let us define `Delta N_(v)`, which is equal to the number of molecules between the velocity range `v` and `v+ Delta v`, given by
`Delta N_(v)=4piNa^(3)e^(-bv^(2))v^(2)Deltav`
where
`N` is total number of molecules
`a=sqrt((M_(0))/(2piRT))` and `b=(M_(0))/(2RT)`
`R` is universal gas constant
`T` is temperature of the gas
`M_(0)` is molecular weight of the gas
Answer the following question:
If `(P)/(P_(c))=P_(r)`, `(T)/(T_(c))=T_(r)`, and `(V_(m))/(V_(m,c))=V_(r)` where

Options

A. `P_(r)` ia reduced pressure, `P_(c)` is critical pressure
B. `T_(r)` ia reduced temperature, `T_(c)` is critical temperature
C. `V_(r)` is reduced volume, `V_(c)` is critical volume
D. then the temperature of state (or van der Waals equation), only in terms of `P_(r)`, `T_(r)`, and `V_(r)` is

Explanation

Use `(P+(a)/(V^(2)))(V_(m)-b)=RT`,
Put `P=P_(c)P_(r)`, `T=T_(r)`,
`V_(m)=V_(m,c)V_(t)`, `P_(c)=(a)/(27b^(2))`, `T_(c)=(8a)/(27Rb)`, and `V_(m,c)=3b`