Question

The speed of sound in oxygen at S.T.P. will be approximately: Given, \( R = 8.3 \, \text{J K}^{-1} \), \( \gamma = 1.4 \))

• A. \( 310 \, \text{m/s} \)
• B. \( 333 \, \text{m/s} \)
• C. \( 341 \, \text{m/s} \)
• D. \( 325 \, \text{m/s} \)

Answer 1

The Correct Option is A

The speed of sound in oxygen at Standard Temperature and Pressure (S.T.P.) is calculated using the formula for gases:

\(v = \sqrt{\frac{\gamma \cdot R \cdot T}{M}}\)

Where:

• \(v\) represents the speed of sound,
• \(\gamma\) (gamma) is the adiabatic index,
• \(R\) is the universal gas constant,
• \(T\) is the absolute temperature,
• \(M\) is the molar mass of oxygen in kg/mol.

The specific values for oxygen and S.T.P. are:

• Adiabatic index, \(\gamma = 1.4\),
• Molar mass of oxygen, \(M = 0.032 \, \text{kg/mol}\),
• Universal gas constant, \(R = 8.3 \, \text{J K}^{-1}\)

At S.T.P., the temperature \(T\) is set to \(273 \, \text{K}\).

Substituting these values into the formula yields:

\(v = \sqrt{\frac{1.4 \cdot 8.3 \cdot 273}{0.032}}\)

The calculation proceeds as follows:

\(v = \sqrt{\frac{3170.44}{0.032}}\)

\(v = \sqrt{99076.25}\)

\(v \approx 314.8 \, \text{m/s}\)

Considering the provided options, the closest value to the calculated result is \(310 \, \text{m/s}\), which serves as the appropriate approximation under these conditions.

The final answer is:

\(310 \, \text{m/s}\)