If the speed of sound in a mixture of 2 moles of Helium and 2 moles of Hydrogen at temperature 972 5 ~K is n 100 ~ms ⁻¹ , then the value of n is (Take, .R= 25 3 ~J ~mol ⁻¹ ~K ⁻¹ )

Step-by-step solution

Given, T= 972 5 ~K , R= 25 3 ~J ~mol ⁻¹ ~K ⁻¹ Molecular mass of the mixture aligned & = n_ He M_ He +n_H M_H n_ He +n_H & n_ He =2 moles, n_H=2 moles & M_ He =4, M_H=2 aligned Molecular mass of the mixtures, aligned M & = 2 4+2 2 2+2 & = 8+4 4 =3 gm / mole aligned Degree of freedom of mixture aligned f= 2 3+2 5 2+2 & =4 f_ mix =1+ 2 f & =1.5 Speed of sound & = f_ mix R T M & = 1.5 25 3 972 5 3 10⁻³ & =900=n 100 ~m / s aligned Hence, n=9