An ideal gas is subjected to a thermodynamic process in which its absolute temperature is doubled and its pressure is quadrupled. If the initial mean free path of the gas molecules is ₀ , what is the final mean free path of the molecules?

Step-by-step solution

The mean free path of a gas molecule is given by: = 1 2 d^2 n From the ideal gas equation, P = n k_B T , the number density n can be written as n = P k_B T . Substituting this into the mean free path formula gives: = k_B T 2 d^2 P This shows that for a given gas, the mean free path is directly proportional to the absolute temperature and inversely proportional to the pressure: T P Given that the final temperature T_f = 2T_i and the final pressure P_f = 4P_i , the new mean free path _f is: _f = ₀ ( T_f T_i ) ( P_i P