The speed of sound in oxygen at S.T.P. will be approximately: (given, $R=8.3 \mathrm{~JK}^{-1}, \gamma=1.4$)

<p>The speed of sound in a gas at standard temperature and pressure (STP) can be calculated using the following formula derived from the ideal gas law and the speed of sound relation in a gas:</p> <p>$v = \sqrt{\gamma \frac{R T}{M}}$</p> <p>Where:</p> <ul> <li>$v$ = speed of sound in the gas</li> <li>$\gamma$ = adiabatic index (ratio of specific heats, $C_p/C_v$)</li> <li>$R$ = universal gas constant</li> <li>$T$ = temperature in Kelvin</li> <li>$M$ = molar mass of the gas in kilograms per mole (kg/mol)</li> </ul> <p>Given:</p> <ul> <li>$R = 8.3 \, J \cdot mol^{-1} \cdot K^{-1}$</li><br/> <li>$\gamma = 1.4$ (For diatomic gases such as oxygen)</li><br/> <li>$T = 273.15 \, K$ (Standard temperature, 0°C in Kelvin)</li><br/> <li>Molar mass of Oxygen ($O_2$) $M = 32 \times 10^{-3} \, kg/mol$ (32 g/mol converted to kg/mol)</li> </ul> <p>Plugging these values into the formula:</p> <p>$v = \sqrt{1.4 \times \frac{8.3 \times 273.15}{32 \times 10^{-3}}}$</p> <p>Calculating the values inside the square root:</p> <p>$v = \sqrt{1.4 \times \frac{2268.745}{0.032}}$</p> <p>$v = \sqrt{1.4 \times 70896.40625}$</p> <p>$v = \sqrt{99304.96875}$</p> <p>$v \approx 315 \, m/s$</p>