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Next: Speed of Sound in Up: Speed of Sound Previous: Introduction   Index

# Speed of sound in ideal and perfect gases

The speed of sound can be obtained easily for the equation of state for an ideal gas (also perfect gas as a sub set) because of a simple mathematical expression. The pressure for an ideal gas can be expressed as a simple function of density, , and a function molecular structure'' or ratio of specific heats, namely

and hence

Remember that is defined for an ideal gas as , and equation (3.12) can be written as

Solution

The solution can be estimated by using the data from steam table3.3
 (3.14)

At and : s = 6.9563 = 6.61376
At and : s = 7.0100 = 6.46956
At and : s = 6.8226 = 7.13216

After interpretation of the temperature:
At and : s 6.9563 6.94199
and substituting into the equation yields

 (3.15)

for ideal gas assumption (data taken from Van Wylen and Sontag, Classical Thermodynamics, table A 8.)

Note that a better approximation can be done with a steam table, and it will be part of the future program (Potto-GDC).

Solution

The temperature is denoted at A'' as and temperature in B'' is . The distance between A'' and B'' is denoted as .

Where the distance is the variable distance. It should be noted that velocity is provided as a function of the distance and not the time (another reverse problem). For an infinitesimal time is equal to

integration of the above equation yields

For assumption of constant temperature the time is

Hence the correction factor
 (3.18)

This correction factor approaches one when .

Next: Speed of Sound in Up: Speed of Sound Previous: Introduction   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21