QJEEM24Ph5a36: JEE Main 2024 Physics - Class 11 JEEM24Ph5a36 Solution: The speed of sound in oxygen at S.T.P. will be approximately:…

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:

$v = \sqrt{\gamma \frac{R T}{M}}$

Where:

• $v$ = speed of sound in the gas
• $\gamma$ = adiabatic index (ratio of specific heats, $C_p/C_v$ )
• $R$ = universal gas constant
• $T$ = temperature in Kelvin
• $M$ = molar mass of the gas in kilograms per mole (kg/mol)

Given:

• $R = 8.3 \, J \cdot mol^{-1} \cdot K^{-1}$


• $\gamma = 1.4$ (For diatomic gases such as oxygen)


• $T = 273.15 \, K$ (Standard temperature, 0°C in Kelvin)


• Molar mass of Oxygen ( $O_2$ ) $M = 32 \times 10^{-3} \, kg/mol$ (32 g/mol converted to kg/mol)

Plugging these values into the formula:

$v = \sqrt{1.4 \times \frac{8.3 \times 273.15}{32 \times 10^{-3}}}$

Calculating the values inside the square root:

$v = \sqrt{1.4 \times \frac{2268.745}{0.032}}$

$v = \sqrt{1.4 \times 70896.40625}$

$v = \sqrt{99304.96875}$

$v \approx 315 \, m/s$