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$$\times {10}^{-3}{m}^3$$

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 $$\rho =\frac{M}{V}=\frac{32g}{22.4\times {10}^{-3}{m}^3}$$

$$Weknowthat:$$ 

$$\frac{C_p}{C_v}=\gamma$$ 

$$\therefore \gamma =\frac{3.5R}{2.5R}=1.4$$ 

$$\text{ Velocity of sound is given by: }$$ 

$$v=\sqrt{\frac{\gamma p}{\rho },}$$ 

$$\text{ where v is the speed of sound . }$$ $$\text{ On substituting the respective values in the above formula, we get: }$$ 

$$v=\frac{1.4\times 1.0\times {10}^5}{\left(\frac{32}{22.4}\right)}$$ 

$$\Rightarrow v=310\text{ m/s }$$

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