Question 282: 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: