Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is 2 times the speed of sound, then the value of n will be

Step-by-step solution

Speed of sound in a gas is given by, v s = γ R T M The formula for RMS speed is, v rms = 3 R T M It is given that v rms = 2 v s ⇒ v s v rms = γ 3 = 1 2 ⇒ γ 3 = 1 2 ⇒ γ = 3 2 For γ of mixture, γ mix = C P , m i x C V , m i x = 2 C P , H + n C P , H e 2 + n 2 C V , H + n C V , H e 2 + n Since Hydrogen is a diatomic gas, C V , H = 5 2 R ,   C P , H = 7 2 R and Helium is monatomic gas, C V , H e = 3 2 R ,   C P , H e = 5 2 R . Therefore, γ mix = 2 C P , H +