Question 244: Thermodynamics & KTG

Question

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

Accepted Answer

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, 0ÃÂ°C in Kelvin)
Molar mass of Oxygen ($$ O_2 $$) $$ M = 32 	imes 10^{-3} \, kg/mol $$ (32 g/mol converted to kg/mol)
Plugging these values into the formula:
$$ v = \sqrt{1.4 	imes \frac{8.3 	imes 273.15}{32 	imes 10^{-3}}} $$
Calculating the values inside the square root:
$$ v = \sqrt{1.4 	imes \frac{2268.745}{0.032}} $$
$$ v = \sqrt{1.4 	imes 70896.40625} $$
$$ v = \sqrt{99304.96875} $$
$$ v \approx 315 \, m/s $$

Answer

341 m/s

Answer

333 m/s

Answer

325 m/s

Answer

315 m/s

Thermodynamics & KTG

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

Choose the correct answer: