Write vanderwaals equation

Van der Waals equation is an equation relating the relationship between the pressure, volume, temperature, and amount of real gases. For a real gas containing ‘n’ moles, the equation is written as;

{tex}\left( P+\frac{a{{n}^{2}}}{{{V}^{2}}} \right)\left( V-nb \right)=n\,R\,T\,(P+V2an2​)(V−nb)=nRT{/tex}

Where, P, V, T, n are the pressure, volume, temperature and moles of the gas. ‘a’ and ‘b’ constants specific to each gas.

The equation can further be written as;

1.  Cube power of volume: {tex}{{V}^{3}}-\left( b+\frac{RT}{P} \right){{V}^{2}}+\frac{a}{P}V-\frac{ab}{P}=0V3−(b+PRT​)V2+Pa​V−Pab​=0{/tex}
2. Reduced equation (Law of corresponding states) in terms of critical constants:

{tex}\left( \pi +\frac{3}{{{\varphi }^{2}}} \right)\left( 3\varphi -1 \right)=8\tau :\,\,where\,\,\pi =\frac{P}{Pc},\varphi =\frac{V}{Vc}\,\,\,and\,\,\tau =\frac{T}{Tc}(π+φ23​)(3φ−1)=8τ:whereπ=PcP​,φ=VcV​andτ=TcT​{/tex}