An ideal gas initially at pressure P and temperature T has a collision frequency f₀ . The gas undergoes a thermodynamic process such that its new pressure becomes 4P and its new temperature becomes 2T . The new collision frequency of the gas molecules will be:

Step-by-step solution

The collision frequency f of a gas molecule is given by the ratio of its average speed v_ avg to its mean free path : f = v_ avg From the kinetic theory of gases, the average speed depends on temperature as: v_ avg T The mean free path depends on temperature and pressure as: T P Substituting these proportionalities into the expression for collision frequency: f T T P f P T Given the initial state (P, T) has frequency f₀ , and the final state is (4P, 2T) with frequency f' : f' f₀ = 4P P T 2T = 4 1 2 = 2 2 Therefore,