# Limitations of Van der waal’s equation

Limitations of  Van der waal’s equation

(i) The value of ‘b’ is not constant but varies with pressure and temperature.

(ii) The value of $V_c$ is not equal to 3b, but actually it is equal to, in some case; and in other cases 2b.

(iii)  The value of $\dfrac{RT_c}{P_cV_c}$ is not equal to $\dfrac{8}{3}$ but it is ususlly more than 3 for most of the gases.

Inversion Temperature:

It is the temperature above which a gas warms up in adiabatic expansion of a gas from high pressure to low pressure. It is denoted by $T_i$ and is related with van der Waals constants as:

$T_i + \dfrac{2a}{bR}$

Boyle’s Temperature:

The temperature at which a real gas obeys Boyle’s law is known as Boyle’s temperature $(T_B)$. It is related with van der Waals constants as:

$T_B = \dfrac{a}{bR}$

Units of van der Waals constants

$a = L^2 atm mol^{-2} \\[3mm] = Nm^4 mol^{-2} \\[3mm] dyne cm^{4} mol^{-2} \\[3mm] b = L mol^{-1} \\[3mm] = m^3 mol^{-1} \\[3mm] = cm^3 mol^{-1}$

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