An ideal gas ( γ = 1.5 ) is expanded adiabatically. How many times its initial volume should the gas be expanded to reduce the root mean square velocity of molecules by a factor of 2 ?

Step-by-step solution

v rms = 3 RT M or v rms ∝ T v rms is to reduce two times, i.e. the temperature of the gas will have to reduce four times or T ' T = 1 4 During the adiabatic process, T ⁡ V ⁡ γ - 1 = T ⁡ ' V ⁡ ' γ - 1 or V ⁡ ' V = T T ' 1 γ - 1 = 4 1 1.5 - 1 = 4 2 = 16 ∴ V ' = 16 V