A sample of oxygen at NTP has volume $V$ and a sample of hydrogen at NTP has volume $4V$. Both the gases are…
A sample of oxygen at NTP has volume $V$ and a sample of hydrogen at NTP has volume $4V$. Both the gases are mixed and the mixture is maintained at NTP. If the speed of sound in hydrogen at NTP is $1270\ \mathrm{ms}^{-1}$, then calculate the speed of sound in mixture.
Solution
Sol. $p_{mix}=\dfrac{p_{O_2}V_{O_2}+p_{H_2}V_{H_2}}{V_{O_2}+V_{H_2}}=\dfrac{16\times V+1\times 4V}{V+4V}=4$
As temperature remains same, therefore pressure will remain constant.
$\therefore\ \dfrac{v_{mix}}{v_{H_2}}=\sqrt{\dfrac{p_{H_2}}{p_{mix}}}=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2}$
$\Rightarrow\ v_{mix}=\dfrac{v_{H_2}}{2}=\dfrac{1270}{2}=635\ \mathrm{ms}^{-1}$
Answer: $635\ \mathrm{ms}^{-1}$