## Speed of Sound in an Ideal Gas

The ideal gas law, expressed in the equationis based on a simple picture of a gas as a large number of molecules which move independently, except for occasional elastic collisions with each other or with the walls of their container.

The ideal gas model predicts that the speed of molecules in a gas composed of a single type of atom is related via the temperatureand massof a molecule throughwhere k is Boltzmann's constant, while the velocity of sound is given by

wherethe ratios of the specific heat capacities at constant pressure and volume, which at room temperature depends mostly on the shape of the molecule.is typically between 1.2 and 1.7, you can see that the rms speed of the molecules is closely related (and slightly larger than) to the speed of sound.

The speed of sound is proportional to the square root of the temperature and inversely proportional to the square root of the mass. The speed increases with temperature because higher temperatures mean faster moving molecules, but decreases with mass because the molecules in ideal gases at the same temperature all have the same kinetic energy (), so increasingmeans decreasing

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