Question

Calculate the speed of sound in oxygen from the following data. The mass of 22.4 litre of oxygen at STP (T = 273 K and p = 1.0 × 10⁵ N m⁻²) is 32 g, the molar heat capacity of oxygen at constant volume is C_v = 2.5 R and that at constant pressure is C_p = 3.5 R.

Answer 1

Given:
Pressure of oxygen p = 1.0 × 10⁵ Nm⁻²
Temperature T = 273 K
Mass of oxygen M = 32 g
Volume of oxygen V = 22.4 litre = 22.4$\times {10}^{-3}{\mathrm{m}}^3$
Molar heat capacity of oxygen at constant volume C_v = 2.5 R
Molar heat capacity of oxygen at constant pressure C_p = 3.5 R
Density of oxygen $\rho =\frac{M}{V}=\frac{32\mathrm{g}}{22.4\times {10}^{-3}{\mathrm{m}}^3}$
$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}: \\ \frac{C_p}{C_v}=\gamma \\ \therefore \gamma =\frac{3.5\mathrm{R}}{2.5\mathrm{R}}=1.4 \\ \mathrm{Velocity}\mathrm{of}\mathrm{sound}\mathrm{is}\mathrm{given}\mathrm{by}: \\ v=\sqrt{\frac{\gamma p}{\rho },} \\ w\mathrm{here}v\mathrm{is}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{sound}. \\ \mathrm{On}\mathrm{substituting}\mathrm{the}\mathrm{respective}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{above}\mathrm{formula},\mathrm{we}\mathrm{get}: \\ v=\frac{1.4\times 1.0\times {10}^5}{\left({\displaystyle \frac{32}{22.4}}\right)} \\ \Rightarrow v=310\mathrm{m}/\mathrm{s} \end{gathered}$$

Therefore, the speed of sound in oxygen is 310 m/s.