Question 224: Thermodynamics & KTG

Question

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

Accepted Answer

The speed of sound in a gas is given by the formula:
$v = \sqrt{\frac{\gamma RT}{M}}$
where $v$ is the speed of sound, $\gamma$ is the adiabatic index, $R$ is the universal gas constant, $T$ is the temperature, and $M$ is the molar mass of the gas.
For diatomic gases, such as hydrogen (HÃ¢ÂÂ) and oxygen (OÃ¢ÂÂ), the adiabatic index $\gamma$ is the same, approximately equal to $\frac{7}{5}$, and the temperature is given as the same for both gases.
Let's denote the speed of sound in hydrogen as $v_	ext{H}$ and in oxygen as $v_	ext{O}$. The ratio of the speeds can be calculated as:
$\frac{v_	ext{H}}{v_	ext{O}} = \sqrt{\frac{M_	ext{O}}{M_	ext{H}}}$
The molar mass of hydrogen (HÃ¢ÂÂ) is $2\, 	ext{g/mol}$, and the molar mass of oxygen (OÃ¢ÂÂ) is $32\, 	ext{g/mol}$.
Now, we can calculate the ratio of the speeds:
$\frac{v_	ext{H}}{v_	ext{O}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$
This means the ratio of the speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is $4:1$.
Therefore, the correct answer is $4:1$.

Answer

$1: 1$

Answer

$1: 2$

Answer

$1: 4$

Answer

$4: 1$

Thermodynamics & KTG

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

Choose the correct answer: