A monoatomic ideal gas has an initial root mean square (RMS) speed of its molecules as v₀ . If the gas is suddenly compressed to 1 8 of its original volume, the new RMS speed of the gas molecules will be:

Step-by-step solution

The sudden compression implies the process is adiabatic. For an adiabatic process, the relationship between temperature and volume is given by: T_i V_i^ -1 = T_f V_f^ -1 For a monoatomic gas, = 5 3 , so - 1 = 2 3 . Given V_f = V_i 8 , we have: T_i V_i^ 2 3 = T_f ( V_i 8 )^ 2 3 T_f = T_i (8)^ 2 3 = T_i (2^3)^ 2 3 = 4T_i From the kinetic theory of gases, the RMS speed of gas molecules is proportional to the square root of the absolute temperature ( v_ rms T ). Therefore, the ratio of the final RMS speed to the initia