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The acoustic relaxation is one important nature of gas, which is caused by the sound propagation in the polyatomic molecule gas. It is the basic relaxation process, which arises from the translational-vibrational degree of freedom (V-T) and the molecular energy transfer between different vibrational degrees of freedom (V-V) separately. By studying the molecule energy transition model of the basic acoustic relaxation processes of gas, we propose an analytic model reflecting the correspondence between effective specific heat capacity and relaxation time in this paper. Compared with the existing relaxation model, the analytic model provides the corresponding relationship between the vibrational specific heat capacity and the relaxation time in V-T and V-V. The solution procedure of the analytic model illustrates that the higher vibrational energy level is the determinant of the basic relaxation process. The effective heat capacity is the foundation of acoustic relaxation attenuation spectrum of gas. The relaxation attenuation spectra result from the analytic model in this paper, which is modified by fine-tuning the collision diameter of the gas molecule, are more consistent with the experiment data than with the existing theoretical value. It proves the correctness and validity of the analytic model.
[1] Hanford A D, O'Connor P D, Anderson J B, Long L N 2008 J. Acoust. Soc. Am. 123 4118
[2] Petculescu A G 2006 J. Optoelectron Adv. M. 8 217
[3] Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) p17
[4] Evans L B, Bass H E, Sutherland L C 1972 J. Acoust. Soc. Am. 51 1565
[5] Bass H E, Baue H J, Evans L B 1972 J. Acoust. Soc. Am. 52 821
[6] Phillips S, Dain Y, Lueptow R M 2003 J. Acoust. Soc. Am. 14 70
[7] Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[8] Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 110 2974
[9] Bass H E, Chambers J P 2001 J. Acoust. Soc. Am. 109 3069
[10] Sutherland L C, Bass H E 2004 J. Acoust. Soc. Am. 115 1012
[11] Petculescu A G, Lueptow R M 2007 Acou. Today 3 17
[12] Zhu M, Wang S, Wang S T, Xia D H 2008 Acta Phy. Sin 57 5749 (in Chinese) [朱明, 王殊, 王菽韬, 夏东海 2008 57 5749]
[13] Holman J P 1980 Thermodynamics (New York: McGraw-Hill) p324
[14] Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[15] Yan S, Wang S 2008 Acta Phy. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
[16] Kinsler W E, Frey A R 1982 Fundamentals of Acoustics (New York: Wiley) p153
[17] Petculescu A G, Lueptow R M 2005 J. Acoust. Soc. Am. 117 175
[18] Herzfeld K F, Litovitz T H 1959 Absorption and dispersion of ultrasonic waves (New York: Academic) p58
[19] Henderson M C, Klose J Z 1959 J. Acoust. Soc. Am. 31 29
[20] Zuckerwar A J, Miller K W 1988 J. Acoust. Soc. Am. 84 970
[21] Liu Z G, Zhang H, Li Y M 2004 Instrument Analysis (Dalian: Dalian University of Technology Press) p255 (in Chinese) [刘志广, 张华, 李亚明 2004 仪器分析 (大连:大连理工大学出版社) 第255页]
[22] Petculescu A G, Hall B, Fraenzle R, Phillips S, Lueptow R M 2006 J. Acoust. Soc. Am. 120 1779
[23] Tabor D 1979 Gases, liquids and solids(Great Britain: Cambridge University Press) p133
[24] Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
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[1] Hanford A D, O'Connor P D, Anderson J B, Long L N 2008 J. Acoust. Soc. Am. 123 4118
[2] Petculescu A G 2006 J. Optoelectron Adv. M. 8 217
[3] Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) p17
[4] Evans L B, Bass H E, Sutherland L C 1972 J. Acoust. Soc. Am. 51 1565
[5] Bass H E, Baue H J, Evans L B 1972 J. Acoust. Soc. Am. 52 821
[6] Phillips S, Dain Y, Lueptow R M 2003 J. Acoust. Soc. Am. 14 70
[7] Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[8] Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 110 2974
[9] Bass H E, Chambers J P 2001 J. Acoust. Soc. Am. 109 3069
[10] Sutherland L C, Bass H E 2004 J. Acoust. Soc. Am. 115 1012
[11] Petculescu A G, Lueptow R M 2007 Acou. Today 3 17
[12] Zhu M, Wang S, Wang S T, Xia D H 2008 Acta Phy. Sin 57 5749 (in Chinese) [朱明, 王殊, 王菽韬, 夏东海 2008 57 5749]
[13] Holman J P 1980 Thermodynamics (New York: McGraw-Hill) p324
[14] Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[15] Yan S, Wang S 2008 Acta Phy. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
[16] Kinsler W E, Frey A R 1982 Fundamentals of Acoustics (New York: Wiley) p153
[17] Petculescu A G, Lueptow R M 2005 J. Acoust. Soc. Am. 117 175
[18] Herzfeld K F, Litovitz T H 1959 Absorption and dispersion of ultrasonic waves (New York: Academic) p58
[19] Henderson M C, Klose J Z 1959 J. Acoust. Soc. Am. 31 29
[20] Zuckerwar A J, Miller K W 1988 J. Acoust. Soc. Am. 84 970
[21] Liu Z G, Zhang H, Li Y M 2004 Instrument Analysis (Dalian: Dalian University of Technology Press) p255 (in Chinese) [刘志广, 张华, 李亚明 2004 仪器分析 (大连:大连理工大学出版社) 第255页]
[22] Petculescu A G, Hall B, Fraenzle R, Phillips S, Lueptow R M 2006 J. Acoust. Soc. Am. 120 1779
[23] Tabor D 1979 Gases, liquids and solids(Great Britain: Cambridge University Press) p133
[24] Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
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