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Vibrational relaxation time is a parameter describing the macroscopic behavior of vibrational energy transition rate between molecular internal degrees of freedom (DOF) and external DOF in excitable gas, which determines the relaxation frequency of the maximum point in acoustic absorption spectrum. To measure the vibrational relaxation time, the traditional methods are used to obtain the acoustic absorption spectra by changing the ambient pressure at several operating frequencies. However, these traditional methods are not suitable for real-time measurement due to the complexity of equipment implementation and the non-ideality of test gas under high pressure. In order to solve those problems, we have developed an algorithm [2013 Meas. Sci. Technol. 24 055002] to capture the primary vibrational relaxation processes only based on the measurements of sound absorption and sound speed at two operating frequencies and a single pressure. But the algorithm only can reconstruct the absorption maximum and it cannot capture the relaxation time with high precision. To measure the frequency dependence of the complex effective specific heat of the relaxing gas, an algorithm synthesizing relaxation processes is given by Petculescu and Lueptow [2005 Phys. Rev. Lett. 94 238301]. In its derivation process, relaxational angular frequency was set to be the inverse ratio to relaxation time. However, the relaxational angular frequency was measured in the adiabatic process of transmission thermodynamic, while the relaxation time was obtained in the thermodynamic isothermal process, the derivation confused the two thermodynamic processes, making the algorithm unable to capture the relaxation frequency with high precision. In order to estimate the relaxation time with higher accuracy, in this paper we first obtain the theoretical relationship among the relaxation times under the three types of thermodynamics conditions, i. e., isothermal, adiabatic constant pressure and adiabatic constant volume. Then we correct the relaxation time derivation and propose our corrected algorithm to reconstruct the relaxation frequencies and relaxation times under the conditions of isothermal, adiabatic constant pressure and adiabatic constant volume. In experiments and simulations, the relaxation times and relaxation frequencies reconstructed by our corrected algorithm for various gas compositions including carbon dioxide, methane, chlorine, nitrogen, and oxygen around room temperature are consistent with the experimental data.
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Keywords:
- relaxation time /
- sound relaxational absorption /
- relaxation process /
- relaxation frequency
[1] Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon)
[2] Schwartz R N, Slawsky Z I, Herzfeld K F 1952 J. Chem. Phys. 20 1591
[3] Tanczos F I 1956 J. Chem. Phys. 25 439
[4] Zhang K S, Ou W H, Jiang X Q, Long F, Hu M Z 2014 J. Korean Phys. Soc. 65 102
[5] Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[6] Zhang K S, Wang S, Zhu M, Ding Y, Hu Y 2013 Chin. Phys. B 22 014305
[7] Zhang K S, Wang S, Zhu M, Hu Y, Jia Y Q 2012 Acta Phys. Sin. 61 174301 (in Chinese) [张克声, 王殊, 朱明, 胡佚, 贾雅琼 2012 61 174301]
[8] Morse P M, Ingard K U 1968 Theoretical Acoustics (New York: McGraw-Hill)
[9] Bhatia A B 1985 Ultrasonic Absorption (New York: Dover)
[10] Mason W P 1965 Physical Acoustics (Vol. II, Pt. A) (New York: Academic Press)
[11] Herzfeld K F, Litovitz T A 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic)
[12] Shields F D 1970 J. Acoust. Soc. Am. 47 1262
[13] Zhang K S, Wang S, Zhu M, Ding Y 2013 Meas. Sci. Technol. 24 055002
[14] Zhang K S, Chen L K, Ou W H, Jiang X Q, Long F 2015 Acta Phys. Sin. 64 054302 (in Chinese) [张克声, 陈刘奎, 欧卫华, 蒋学勤, 龙飞 2015 64 054302]
[15] Hu Y, Wang S, Zhu M, Zhang K S, Liu T T, Xu D Y 2014 Sens. Actuat. B: Chem. 203 1
[16] Bass H E, Sutherland L C, Piercy J, Evans L (in Mason W P, Thurston R N (Vol. XVII) Ed.) 1984 Absorption of Sound by the Atmosphere in Physical Acoustics (Orlando: Academic)
[17] Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[18] Bass H E, Bauer H J, Evans L B 1972 J. Acoust. Soc. Am. 52 821
[19] Shields F D 1960 J. Acoust. Soc. Am. 32 180
[20] Angona F A 1953 J. Acoust. Soc. Am. 25 1116
[21] Bass H E 1973 J. Chem. Phys. 58 4783
[22] Petculescu A G, Hall B, Fraenzle R, Phillips S, Lueptow R M 2006 J. Acous. Soc. Am. 120 1779
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[1] Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon)
[2] Schwartz R N, Slawsky Z I, Herzfeld K F 1952 J. Chem. Phys. 20 1591
[3] Tanczos F I 1956 J. Chem. Phys. 25 439
[4] Zhang K S, Ou W H, Jiang X Q, Long F, Hu M Z 2014 J. Korean Phys. Soc. 65 102
[5] Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[6] Zhang K S, Wang S, Zhu M, Ding Y, Hu Y 2013 Chin. Phys. B 22 014305
[7] Zhang K S, Wang S, Zhu M, Hu Y, Jia Y Q 2012 Acta Phys. Sin. 61 174301 (in Chinese) [张克声, 王殊, 朱明, 胡佚, 贾雅琼 2012 61 174301]
[8] Morse P M, Ingard K U 1968 Theoretical Acoustics (New York: McGraw-Hill)
[9] Bhatia A B 1985 Ultrasonic Absorption (New York: Dover)
[10] Mason W P 1965 Physical Acoustics (Vol. II, Pt. A) (New York: Academic Press)
[11] Herzfeld K F, Litovitz T A 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic)
[12] Shields F D 1970 J. Acoust. Soc. Am. 47 1262
[13] Zhang K S, Wang S, Zhu M, Ding Y 2013 Meas. Sci. Technol. 24 055002
[14] Zhang K S, Chen L K, Ou W H, Jiang X Q, Long F 2015 Acta Phys. Sin. 64 054302 (in Chinese) [张克声, 陈刘奎, 欧卫华, 蒋学勤, 龙飞 2015 64 054302]
[15] Hu Y, Wang S, Zhu M, Zhang K S, Liu T T, Xu D Y 2014 Sens. Actuat. B: Chem. 203 1
[16] Bass H E, Sutherland L C, Piercy J, Evans L (in Mason W P, Thurston R N (Vol. XVII) Ed.) 1984 Absorption of Sound by the Atmosphere in Physical Acoustics (Orlando: Academic)
[17] Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[18] Bass H E, Bauer H J, Evans L B 1972 J. Acoust. Soc. Am. 52 821
[19] Shields F D 1960 J. Acoust. Soc. Am. 32 180
[20] Angona F A 1953 J. Acoust. Soc. Am. 25 1116
[21] Bass H E 1973 J. Chem. Phys. 58 4783
[22] Petculescu A G, Hall B, Fraenzle R, Phillips S, Lueptow R M 2006 J. Acous. Soc. Am. 120 1779
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