My name is Alexander FufaeV and here I write about:
Van der Waals Equation: How to Describe Real Gas
Important Formula
$$\mathit{\Pi} ~=~ \frac{n \, R \, T}{V ~-~ n \, V_{\text b}} ~-~ \frac{n^2 \, a}{V^2}$$
$$\mathit{\Pi} ~=~ \frac{n \, R \, T}{V ~-~ n \, V_{\text b}} ~-~ \frac{n^2 \, a}{V^2}$$
$$T ~=~ \frac{ V ~-~ n \, V_{\text b} }{ n \, R } \, \left( \mathit{\Pi} + \frac{n^2 \, a}{V^2} \right) $$
$$V_{\text b} ~=~ V ~-~ \frac{ n \, R \, T }{ \mathit{\Pi} ~+~ \frac{n^2 \, a}{V^2} }$$
$$a ~=~ \left( \frac{n \, R \, T}{V ~-~ n \, V_{\text b}} ~-~ \mathit{\Pi} \right) \, \frac{V^2}{n^2}$$
What do the formula symbols mean?
Pressure
$$ \mathit{\Pi} $$ Unit $$ \mathrm{Pa} $$
Pressure of the (real) gas. With the real gas - in contrast to the ideal gas - the gas pressure may be very high.
Temperature
$$ T $$ Unit $$ \mathrm{K} $$
Temperature of the (real) gas. With the real gas - in contrast to the ideal gas - the temperature of the gas may be low.
Volume
$$ V $$ Unit $$ \mathrm{m}^3 $$
Volume of the (real) gas. Molar volume: \( V_{\text m} ~=~ \frac{V}{n} \).
Amount of substance
$$ n $$ Unit $$ \mathrm{mol} $$
Amount of substance indirectly indicates the number of particles of the gas.
Covolume
$$ V_{\text b} $$
Covolume is the material-dependent intrinsic volume of the particles of the real gas. It reduces the volume \( V \) available for the motion of the particles to \( (V ~-~ n\,V_{\text b}) \). For the ideal gas, the following holds: \( V_{\text b} ~=~ 0 \). The unit of covolume is \( \mathrm{m}^3 / \mathrm{mol} \).
Cohesion parameter
$$ a $$
Cohesion parameter is a material-dependent quantity that indicates the force between the particles of the gas. In the case of an ideal gas, the following holds true: \( a ~=~ 0 \). The term \( \frac{n^2 \, a}{V^2} \) is called internal pressure. The unit of the cohesion parameter is \( \mathrm{Pa}\,\mathrm{m}^6 / \mathrm{mol}^2 \).
Gas constant
$$ R $$ Unit $$ \frac{\mathrm J}{\mathrm{mol} \, \mathrm{K}} $$Molar gas constant (also called universal gas constant) is a physical constant from thermodynamics and has the following exact value:
$$ R ~=~ 8.314 \, 462 \, 618 \, 153 \, 24 \, \frac{\mathrm J}{\mathrm{mol} \, \mathrm{K}} $$
The Van der Waals equation is designed for real gases and introduces corrections to the ideal gas equation in order to describe the behavior of real gases more precisely.
$$ \begin{align} \mathit{\Pi} ~=~ \frac{n \, R \, T}{V ~-~ n \, V_{\text b}} ~-~ \frac{n^2 \, a}{V^2} \end{align} $$
The equation thus modifies the volume \( V \) and the pressure \( \mathit{\Pi} \) compared to the ideal gas equation to take into account the effects of molecular size and attractive forces.