The Speed of Sound in Gases

Oct 13, 2025 by miodeya.com 36 views

Introduction

The velocity of sound in a gas is a fundamental concept in physics that has numerous applications in various fields, including acoustics, engineering, and meteorology. The velocity of sound in a gas is determined by its physical properties, such as temperature, pressure, and molecular weight. In this article, we will explore the ratio of the velocity of sound in helium gas to that in nitrogen gas at a given temperature.

The Speed of Sound in Gases

The speed of sound in a gas is given by the equation:

c = √(γRT/M)

where c is the speed of sound, γ is the adiabatic index, R is the gas constant, T is the temperature in Kelvin, and M is the molecular weight of the gas.

Adiabatic Index (γ)

The adiabatic index (γ) is a dimensionless quantity that depends on the specific heat capacity of the gas. For a monatomic gas like helium, γ = 5/3, while for a diatomic gas like nitrogen, γ = 7/5.

Molecular Weight (M)

The molecular weight of a gas is the sum of the atomic weights of its constituent atoms. The molecular weight of helium (He) is 4 g/mol, while that of nitrogen (N2) is 28 g/mol.

Temperature (T)

The temperature of the gas is assumed to be constant in this analysis.

Calculating the Ratio of Velocities

Using the equation for the speed of sound, we can calculate the ratio of the velocity of sound in helium gas to that in nitrogen gas:

cHe / cN2 = √(γHe RT/MHe) / √(γN2 RT/MN2)

Substituting the values of γ, R, T, MHe, and MN2, we get:

cHe / cN2 = √((5/3)RT/4) / √((7/5)RT/28)

Simplifying the expression, we get:

Q&A: The Velocity of Sound in Gases

Q: What is the velocity of sound in a gas? A: The velocity of sound in a gas is a fundamental concept in physics that has numerous applications in various fields, including acoustics, engineering, and meteorology. The velocity of sound in a gas is determined by its physical properties, such as temperature, pressure, and molecular weight.

Q: How is the velocity of sound in a gas calculated? A: The velocity of sound in a gas is given by the equation:

c = √(γRT/M)

where c is the velocity of sound, γ is the adiabatic index, R is the gas constant, T is the temperature in Kelvin, and M is the molecular weight of the gas.

Q: What is the adiabatic index (γ)? A: The adiabatic index (γ) is a dimensionless quantity that depends on the specific heat capacity of the gas. For a monatomic gas like helium, γ = 5/3, while for a diatomic gas like nitrogen, γ = 7/5.

Q: What is the molecular weight (M) of a gas? A: The molecular weight of a gas is the sum of the atomic weights of its constituent atoms. The molecular weight of helium (He) is 4 g/mol, while that of nitrogen (N2) is 28 g/mol.

Q: How does the temperature (T) affect the velocity of sound in a gas? A: The temperature of the gas is assumed to be constant in this analysis. However, in reality, the temperature can affect the velocity of sound in a gas.

Q: What is the ratio of the velocity of sound in helium gas to that in nitrogen gas? A: Using the equation for the speed of sound, we can calculate the ratio of the velocity of sound in helium gas to that in nitrogen gas:

cHe / cN2 = √(γHe RT/MHe) / √(γN2 RT/MN2)

Substituting the values of γ, R, T, MHe, and MN2, we get:

cHe / cN2 = √((5/3)RT/4) / √((7/5)RT/28)

Simplifying the expression, we get:

cHe / cN2 = √(5/3 × 28 / 4 × 7/5) = √(5/3 × 7/4) = √(35/12) = √(35/12) × √(12/12) = √(420/144) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12) × √(4/4) = √(140/48) = √(35/12)