The speed of sound in air derived with ideal and real gas behaviorSpenser Joyce

11-5-2014

Physics Comprehensive

• = 1 + …Truncate at B

•Sub in V =

•Expansion:[1+}]

Derivation of Coefficients

From Cramer paper and references

• = 1.4029

• R = 8.31448

• M = 28.9643704*

• p = 101325 Pa

• T = 273.15 K

B = -13.5* = 66* = -155*

• = 331.6648

• -11.51

• 10.25

• -9.382

Departures from ideal gas behavior:

[1+}]

Ideal gas behavior, p = 101325 Pa and T is variable

K temps

Non-ideal behavior including second virial

coefficient B

Temperature (K) Temperature (ºC)

Speed o

f Sound

(m/s

)

Speed o

f Sound (

m/s

)

*Cramer valid only for temps 0ºC-30ºC

*Greenspan paper

• –2.0739* • *

References• Cramer, Owen. "The variation of the specific-heat ratio and the speed

of sound in air with temperature, pressure, humidity, and CO2 concentrations." Journal of the Acoustical Society of America 93.5 (1993): 2510-2516. Print.

• Bird, R. Byron, Charles F. Curtiss, and Joseph O. Hirschfelder. Molecular Theory of Gases and Liquids. New York: n.p., 1954. Print.

• Wong, George S. K. “Speed of sound in standard air.” Journal of the Acoustical Society of America 79 (1986): 1359-1366. Print.

• Greenspan, Martin. “Comments on “Speed of sound in standard air” [J. Acoust. Soc. Am. 79, 1359-1366 (1986)].” Journal of the Acoustical Society of America 82 (1987): 370-372. Print.

Questions?