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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 Cv = 2.5 R and that at constant pressure is Cp = 3.5 R.
Solution
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 Cv = 2.5 R
Molar heat capacity of oxygen at constant pressure Cp = 3.5 R
Density of oxygen \[\rho = \frac{M}{V} = \frac{32 g}{22 . 4 \times {10}^{- 3} m^3}\]
\[We know that: \]
\[\frac{C_p}{C_v} = \gamma\]
\[ \therefore \gamma = \frac{3 . 5 R}{2 . 5 R} = 1 . 4\]
\[\text { Velocity of sound is given by: }\]
\[ v = \sqrt{\frac{\gamma p}{\rho},}\]
\[\text { where v is the speed of sound . }\] \[\text { On substituting the respective values in the above formula, we get: }\]
\[ v = \frac{1 . 4 \times 1 . 0 \times {10}^5}{\left( \frac{32}{22 . 4} \right)}\]
\[ \Rightarrow v = 310 \text { m/s }\]
Therefore, the speed of sound in oxygen is 310 m/s.
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