Question

The speed of a longitudinal wave in a mixture containing 4 moles of He and 1 mole of Ne at 300 K will be

• A. 930 m/s
  
• B. 541 m/s
  
• C. 498 m/s
  
• D. None of these
  

Answer 1

The correct option is A 930 m/s

The mixture contains $n_1=4mol$ of $He$ and $n_2=4mole$ of $Ne$ act. $T=300K$.

Forth $He$ and $Ne$ are monoatomic, so we take $r$ mix $=5/3[r=\frac{cp}{cv}]$

$M^{\prime }=\frac{M_1{n}_1+M_2{n}_2}{n_1+n_2}$

$=\frac{4\times 4+20\times 1}{4+1}=\frac{24}{5}=4.8g/mol$

$=4.8\times {10}^{-3}kg/mol$

$\therefore$ Speed of sound through mixture

$v=\sqrt{\frac{vRT}{M^{\prime }}}=\sqrt{\frac{5}{3}\times \frac{8.3\times 300}{4.8\times {10}^{-3}}}\sim 929.83m/s$