A monatomic ideal gas initially has a collision frequency Z₀ among its molecules. The gas undergoes a sudden adiabatic expansion to 8 times its original volume. The new collision frequency of the molecules will be

Step-by-step solution

The collision frequency is given by Z = 2 d^2 n v For a fixed mass of gas, the number density n 1 V and the average speed v T . Thus, Z T V For an adiabatic process, T V^ - 1 = constant , which means T V^ 1 - . Substituting this into the proportionality for Z : Z V^ 1 - V = V^ 1 - 2 - 1 = V^ - + 1 2 For a monatomic ideal gas, the ratio of specific heats is = 5 3 . The exponent of V becomes - 5 3 + 1 2 = - 4 3 . Therefore, Z V^ -4/3 . When the volume is increased to 8 times its original value ( V_f = 8 V_i ): Z_f =