气体声弛豫过程中有效比热容与弛豫时间的分解对应关系

贾雅琼; 王殊; 朱明; 张克声; 袁飞阁

doi:10.7498/aps.61.095101

摘要

声在多原子分子气体中传播所引起的弛豫过程是探索气体特性的重要方面. 本文通过研究气体声弛豫过程中振动自由度与平动自由度(V-T)以及振动自由度之间(V-V)的分子能量转移模型, 给出了有效比热容与弛豫时间的分解对应关系及其通用获得方法. 该分解模型与现有的声弛豫模型相比, 反映了分解后的V-T 和V-V弛豫过程中振动比热容与弛豫时间的对应关系, 并发现了较高能级是引起对应声弛豫过程的决定因素. 将基于该分解模型获得的气体声弛豫衰减谱经碰撞直径微调改进后, 比现有理论更接近实验数据, 其结果证明了该分解对应关系的正确性和合理性.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
华中科技大学电子与信息工程系, 武汉 430074;

2.
湖南工学院电气与信息工程系, 衡阳 421002

基金项目: 国家自然科学基金(批准号: 60971009, 61001011), 高等学校博士学科点专项科研基金(批准号: 20090142110019)和湖北省自然科学基金(批准号: 2010CDB02701)资助的课题.

Authors and contacts

1.
Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;

2.
Department of Electronics and Information Engineering, Hunan Institute of Technology, Hengyang 421002, China

Funds: Project supported by the National Natural Science Foundation of China(Grant Nos. 60971009, 61001011), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20090142110019), and the Hubei Natural Science Foundation(Grant No. 2010CDB02701).

参考文献

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[2]	Petculescu A G 2006 J. Optoelectron Adv. M. 8 217
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[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

施引文献

[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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