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For the same pressure and density, the speed of sound is highest in a (a) Monoatomic gas (b) Diatomic gas (c) Triatomic gas (d) Polyatomic gas

nainika , 9 Years ago

Grade 12th pass

1 Answers

Askiitians Tutor Team

The speed of sound in a gas is influenced by several factors, including the type of gas and its molecular structure. When comparing monoatomic, diatomic, triatomic, and polyatomic gases, the speed of sound is highest in a monoatomic gas. Let’s break down why this is the case.

Understanding the Speed of Sound

The speed of sound in a gas can be expressed using the formula:

c = √(γRT/M)

In this equation:

c is the speed of sound.
γ (gamma) is the adiabatic index, which is the ratio of specific heats (Cp/Cv).
R is the universal gas constant.
M is the molar mass of the gas.

Molecular Structure and Its Impact

The molecular structure of a gas significantly affects its specific heats and, consequently, the value of γ. Here’s how different types of gases compare:

Monoatomic gases: These gases consist of single atoms, such as helium or neon. They have the simplest structure, leading to a higher γ value (approximately 5/3). This higher value results in a greater speed of sound.

Diatomic gases: Gases like oxygen (O2) and nitrogen (N2) are diatomic. They have more complex molecular structures, which means their γ is lower (approximately 7/5). This results in a slower speed of sound compared to monoatomic gases.

Triatomic gases: These include gases like carbon dioxide (CO2) and water vapor (H2O). Their γ is even lower due to additional degrees of freedom (vibrational modes), which further decreases the speed of sound.

Polyatomic gases: These gases have multiple atoms and exhibit even more complexity in their molecular structure. Their γ values are typically lower than those of triatomic gases, resulting in the slowest speed of sound among the four categories.

Why Monoatomic Gases Excel

The reason monoatomic gases have the highest speed of sound lies in their simplicity. With fewer degrees of freedom, they can transmit sound waves more efficiently. In contrast, diatomic and polyatomic gases have additional vibrational and rotational modes that absorb energy, which reduces the speed of sound.

Practical Examples

To illustrate, consider helium (a monoatomic gas) and air (a mixture of diatomic gases). Helium has a speed of sound of about 972 m/s at room temperature, while the speed of sound in air is approximately 343 m/s. This significant difference highlights how molecular structure impacts sound propagation.

In summary, for the same pressure and density, the speed of sound is highest in a monoatomic gas due to its simple atomic structure and higher adiabatic index, allowing for more efficient sound wave transmission. This understanding is crucial in fields ranging from acoustics to atmospheric science, where sound propagation plays a vital role.