The density of air at NTP is $1.29\ \mathrm{kg\ m}^{-3}$. Assume air to be diatomic with $\gamma=1.4$. What…
The density of air at NTP is $1.29\ \mathrm{kg\ m}^{-3}$. Assume air to be diatomic with $\gamma=1.4$. What will be the velocity of sound at $127^\circ\mathrm{C}$?
Solution
Sol. According to Laplace formula, speed of sound in air at NTP,
$v=\sqrt{\frac{\gamma p}{\rho}}=\sqrt{\frac{1.4\times1.013\times10^5}{1.29}}$
$=331.6\ \mathrm{ms}^{-1}$
As, the velocity of sound is proportional to the square root of absolute temperature.
$\Rightarrow \dfrac{v_2}{v_1}=\sqrt{\dfrac{T_2}{T_1}}\Rightarrow v_2=v_1\sqrt{\dfrac{T_2}{T_1}}=331.6\sqrt{\dfrac{273+127}{273+27}}$
$v_2=382.8\ \mathrm{ms}^{-1}$
Answer: $382.8\ \mathrm{ms}^{-1}$