An ideal gas ( γ = 1.5 ) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2 times?

Question

An ideal gas ( γ = 1.5 ) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2 times?, 4 times, 16 times, 8 times, 2 times

MARKS App · Accepted Answer

v r m s = 3 R T M o r v r m s ∝ T v r m s is to reduce two times, i e , the temperature of the gas will have to reduce four times or T ′ T = 1 4 During 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

Search any question & find its solution

Looking for more such questions to practice?