Compare values of the speed of sound in m / s at 20^∘ C in the following gases: (a) air, (b) car

step 1 For part A, we have that C equals the root of 287 times 293 times 1 .4 equals 343 meters per sec

Compare values of the speed of sound in m / s at 20^∘ C in...

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance and plays a critical role in determining the speed of sound in gases. In the speed of sound equation, a lower molar mass (M) leads to a higher propagation speed because lighter molecules respond more quickly to pressure disturbances. Therefore, gases like helium, with a low molar mass, will generally have a higher speed of sound compared to heavier gases.

Temperature Effects

Temperature significantly influences the speed of sound in gases because it affects the kinetic energy of the gas molecules. Higher temperatures increase the average speed of molecules, which in turn speeds up the propagation of sound waves. In analyzing sound speed at a specific temperature, it is important to convert to the absolute scale (Kelvin) to apply the physical laws accurately.

Speed of Sound in Gases

The speed of sound in a gas is the speed at which small pressure disturbances propagate through the medium. It is typically calculated using an equation of the form c = ?(?RT/M), where ? represents the adiabatic index, R is the universal gas constant, T is the absolute temperature, and M is the molar mass of the gas. This concept is essential for comparing how quickly sound travels in different gases under the same temperature conditions.

Adiabatic Index

The adiabatic index, represented by ?, is the ratio of specific heats at constant pressure and volume (Cp/Cv). It is a key parameter in the speed of sound formula because it reflects how a gas responds to compression and expansion. Different gases have different ? values based on their degrees of freedom and molecular structure, thus affecting the rate at which sound can propagate through them.

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