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

Answer: (A)

$310 \, \text{m/s}$

Answer 2

The speed of sound v in a gas is given by:

$v = \sqrt{\frac{\gamma RT}{M}},$

where:

• $\gamma$ is the adiabatic index (or ratio of specific heats, $C_p/C_v$),
• $R$ is the universal gas constant,
• $T$ is the absolute temperature in Kelvin,
• $M$ is the molar mass of the gas in kg/mol.

We are given:

$\gamma = 1.4, \quad R = 8.3 \, \text{J/K mol}, \quad T = 273 \, \text{K}, \quad M = 32 \times 10^{-3} \, \text{kg/mol}.$

Substitute these values into the formula:

$v = \sqrt{\frac{1.4 \times 8.3 \times 273}{32 \times 10^{-3}}}.$

Calculate the expression inside the square root:

$1.4 \times 8.3 = 11.62,$

$11.62 \times 273 = 3173.26,$

$\frac{3173.26}{32 \times 10^{-3}} = 99164.375.$

Now take the square root to find v :

$v = \sqrt{99164.375} \approx 315 \, \text{m/s}.$

The closest answer to this calculated value is: 310 m/s.