Find speed of sound in hydrogen gas at 27°C, if $C_p/C_V$ for H$_2$ is 1.4. Gas constant, $R=8.31\…
Find speed of sound in hydrogen gas at 27°C, if $C_p/C_V$ for H$_2$ is 1.4. Gas constant, $R=8.31\ \mathrm{J\ mol}^{-1}\ \mathrm{K}^{-1}$.
Solution
Sol. The speed sound in a gas, $v=\sqrt{\gamma p/\rho}$
$\therefore\quad v=\sqrt{\dfrac{\gamma RT}{M}}\qquad(\because\ pV=RT\ \text{and}\ \rho=\dfrac{M}{V})$
Here, $T = 27 + 273 = 300\ \text{K},\ \gamma = \dfrac{C_p}{C_v} = 1.4,$
$R = 8.31\ \text{J mol}^{-1}\ \text{K}^{-1},$
$M = 2\times 10^{-3}\ \text{kg mol}^{-1}$
$\therefore\quad v=\sqrt{\dfrac{1.4\times 8.31\times 300}{2\times 10^{-3}}}=1321\ \text{ms}^{-1}$
Note In the above formula, put $M = 2 \times 10^{-3}kg mol^{-1}$. Do not put it 2 kg.
Answer: $1321\ \text{ms}^{-1}$
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