The ideal gas and small deviation from ideality

Theoretically, an ideal gas is a hypothetical system of noninteracting molecules, i.e., 

In practice, the ideal-gas behavior is obtained in the limit of very low densities or pressure, where interactions between the (real) molecules are on the average negligible. One should be careful, however, to distinguish between these two conditions for ideality. The two systems are not identical, as we shall see later in the book. 

Using (1.76) in the classical partition function (1.67), we immediately obtain 

For simple spherical particles, sometimes referred to as structureless particles, equation (1.77) reduces to 

Note that q and A depend on the temperature and not on the volume V or on N. An important consequence of this is that the equation of state of an ideal gas is independent of the particular molecules constituting the system. To see this, we derive the expression for the pressure. Differentiating (1.77) with respect to volume, we obtain 

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