$b_m=\displaystyle\frac{4\pi}{3}r_0^3$

b_m=\displaystyle\frac{4\pi}{3}r_0^3

$ a_m =\displaystyle\frac{3}{ s -3} u_0 b_m $

a_m = 3* u_0 * b_m/( s -3)

$(\bar{p}+a_mc^2)\left(\displaystyle\frac{1}{c}-b_m\right)=kT$

( bp + a_mc ^2)*(1/ n - b_m )= k_B * T

$ a_m =\displaystyle\frac{4 \pi r_0^3}{ s -3} u_0 $

a_m = 4* pi * r_0 ^3* u_0 /( s -3)

$n=\displaystyle\frac{N}{N_A}$

n = N / N_A

$ v =\displaystyle\frac{ V }{ n }$

v = V / n

$c=\displaystyle\frac{N_A}{v}$

c = N_A / v

$\left(\bar{p}+\displaystyle\frac{a}{v^2}\right)(v-b)=RT$

\left(\bar{p}+\displaystyle\frac{a}{v^2}\right)(v-b)=RT

$ R = k_B N_A $

R = k_B * N_A

$a=N_A^2a_m$

a = N_A ^2* a_m

$b=N_Ab_m$

b=N_Ab_m

$ B_2 = b_m \left(1-\displaystyle\frac{1}{ k_B T }\displaystyle\frac{ a_m }{ b_m }\right)$

B_2 = b_m *(1- a_m /( k_B * T * b_m ))

$\displaystyle\frac{\bar{p}}{kT}=c+b_m\left(1-\displaystyle\frac{1}{kT}\displaystyle\frac{a_m}{b_m}\right)c^2$

\displaystyle\frac{\bar{p}}{kT}=c+b_m\left(1-\displaystyle\frac{1}{kT}\displaystyle\frac{a_m}{b_m}\right)c^2

$c=\displaystyle\frac{nN_a}{V}$

c = N_a / v

$\displaystyle\frac{\bar{p}}{kT}=c$

\displaystyle\frac{\bar{p}}{kT}=c

$pV=nkN_AT$

pV=nkN_AT