The compressibility factor for a definite amount of a Van der Waals' gas at ${\mathrm{0}}^{\circ }\mathrm{C}$ and $100 \mathrm{atm}$ is found to be $0.5.$ Assuming the volume of gas molecules negligible, the Van der Waals' constant $\text{'}\mathrm{a}\text{'}$ for a gas is:

The unit of the van der Waals gas equation parameter $\text{'}\mathrm{a}\text{'}$ in $\left(\mathrm{P}+\frac{{\mathrm{an}}^2}{{\mathrm{V}}^2}\right)(\mathrm{V}-\mathrm{nb})=\mathrm{nRT}$ is:

In thermodynamics, the $\mathrm{P}-\mathrm{V}$ work done is given by $\mathrm{w}=-\int {\mathrm{dVP}}_{\mathrm{ext}}$. For a system undergoing a particular process, the work done is,

$\mathrm{w}=-\int \mathrm{dV}\left(\frac{\mathrm{RT}}{\mathrm{V}-\mathrm{b}}-\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)$. This equation is applicable to a

For a van der Waals' gas, the term $\left(\frac{\mathrm{ab}}{{\mathrm{V}}^2}\right)$ represents some