The relationship between ${\mathrm{P}}_{\mathrm{c}},{\mathrm{V}}_{\mathrm{c}}$ $\text{ and }$${\mathrm{T}}_{\mathrm{c}}$

${\mathrm{T}}_{\mathrm{c}}$= Temperature of gas

${\mathrm{V}}_{\mathrm{c}}$=Volume of gas

${\mathrm{P}}_{\mathrm{c}}$=pressure of gas

Relationship between ${\mathrm{P}}_{\mathrm{c}},{\mathrm{V}}_{\mathrm{c}}$ $\text{ and }$${\mathrm{T}}_{\mathrm{c}}$

${\mathrm{T}}_{\mathrm{c}}=\frac{8}{27}\frac{\mathrm{a}}{\mathrm{Rb}}$

$\mathrm{a}=\frac{27}{8}{\mathrm{T}}_{\mathrm{c}}\mathrm{Rb}$

$\begin{array}{l}{\mathrm{V}}_{\mathrm{c}}=3\mathrm{b}\\ \mathrm{b}=\frac{{\mathrm{V}}_{\mathrm{c}}}{3}\end{array}$

${\mathrm{P}}_{\mathrm{c}}=\frac{\mathrm{a}}{27{\mathrm{b}}^2}$

Put a, b values in the equation

${\mathrm{p}}_{\mathrm{c}}=\frac{27{\mathrm{T}}_{\mathrm{c}}\mathrm{Rb}}{8\times 27\times {\mathrm{b}}^2}$

${\mathrm{p}}_{\mathrm{c}}=\frac{27{\mathrm{T}}_{\mathrm{c}}\mathrm{Rb}}{8\times 27\times \frac{{\mathrm{v}}_{\mathrm{c}}}{3}}$

Therefore the correct option is D