Question

The speed of sound through oxygen gas at T K is $vm{s}^{-1}$. As the temperature becomes 2T and oxygen gas dissociated into atomic oxygen, the speed of sound:

• A. remains the same
• B. becomes 2v
• C. becomes $\sqrt{2}v$
• D. none of these

Answer 1

Answer: (D)

none of these

Oxygen molecule is diatomic $\left(O_2\right)$ so has $r_1=\frac{7}{5}$ while atomic oxygen is mono atomic and so has $r_2=\frac{5}{3}$

So, speed of sound :- $m{O}_2$

$v=\sqrt{\frac{r_{1}R{T}_A}{M_1}}$, where $M_1=$ molar mass of $O_2=32g/mol$

$=0.032kg/mol$

while in nascent oxygen (O),

$v^{\prime }=\sqrt{\frac{r_{2}R{T}_2}{M_2}}$ $T_2=2T$ (given)

taking ration and $M_2=$ atomic mass of $O=0.016kg/mol$

$\frac{v^{\prime }}{v}=\sqrt{\frac{M_2{r}_{1}T}{M_1{r}_2\left(2T\right)}}$ $\Rightarrow \frac{M_2}{M_1}=2$

$=\sqrt{\frac{2}{2}\times \frac{7}{5}\times \frac{5}{3}}=\sqrt{\frac{7}{3}}\Rightarrow v^{\prime }=v\sqrt{\frac{7}{3}}$