vander waal equation and critical constant

the equation of state for critical gas can be written as ( p + a/v2 )(v-b)=RT =

......................................1

at critical point Xc, we have  ; critical temperature, volume and pressure , and their values can be calculated as follows ,

equation 1 ,can be written as

.................................2

...................................3

differentiating equation 2 we get

dividing

 ........................................5

substituting the value of Vc in 2 we have

→ ............................................6

Again substituting  the values of Vc and Tc in equation 2 to get

 ......................................................................7