Two moles of helium are mixed with n moles of hydrogen. The root mean square (rms) speed of gas molecules in the mixture is 2 times the speed of sound in the mixture. Then, the value of n is

Step-by-step solution

v_ mis = 3 R T M and v_ sound = R T M , v_ rms =2 v_ sound i.e. = 3 2 = ratio of C_p C_V for the mixture C_V= n₁ C_ V₁ +n₂ C_ V₂ n₁+n₂ and C_p= n₁ C_ p₁ +n₂ C_ p₂ n₁+n₂ = C_P C_V = n₁ C_ p₁ +n₂ C_ p₂ n₁ C_ V₁ +n₂ C_ V₂ 3 2 = 2 ( 5 2 R )+n ( 7 2 R ) 2 ( 3 2 R )+n ( 5 2 R ) array ll & 3 2 = 10+7 n 6+5 n & n=2 array