The compressibility factor (Z) is defined as:
\( Z = \frac{PV}{RT} \)
For a van der Waals gas, the equation of state is:
\( \left(P + \frac{a}{V^2}\right)(V - b) = RT \)
At high pressures, the volume V decreases, making the term b (excluded volume) significant. The term involving a (intermolecular attraction) becomes negligible. Simplifying for high pressure:
\( Z \approx 1 + \frac{Pb}{RT} \)
Thus, the compressibility factor is approximately \( 1 + \frac{Pb}{RT} \) under high-pressure conditions.
Two statements are given below: Statement-I: The ratio of the molar volume of a gas to that of an ideal gas at constant temperature and pressure is called the compressibility factor.
Statement-II: The RMS velocity of a gas is directly proportional to the square root of \( T(K) \).