Question

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

• A. 4 : 1
• B. 1 : 2
• C. 1 : 1
• D. 1 : 4

Answer 1

The Correct Option is A

To determine the ratio of the speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature, we need to understand the formula for the speed of sound in a gas, which is given by:

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

where:

• \(v\) is the speed of sound in the gas,
• \(\gamma\) (gamma) is the adiabatic index, also known as the heat capacity ratio,
• \(R\) is the universal gas constant,
• \(T\) is the absolute temperature in Kelvin,
• \(M\) is the molar mass of the gas.

The speed of sound is inversely proportional to the square root of the molar mass of the gas under the same temperature and pressure conditions. Thus, the ratio of the speed of sound in two gases with molar masses \(M_1\) and \(M_2\) can be expressed as:

\(\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}\)

Given:

• The molar mass of hydrogen \((H_2)\) is approximately 2 g/mol,
• The molar mass of oxygen \((O_2)\) is approximately 32 g/mol.

Substituting these values into the formula, we find:

\(\frac{v_{\text{hydrogen}}}{v_{\text{oxygen}}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4\)

Therefore, the speed of sound in hydrogen gas is 4 times the speed of sound in oxygen gas at the same temperature. The correct answer is 4 : 1.