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In thermodynamics, the complete equation of state (EOS) for closed system is a functional relation defined by two independent state variables, and all other thermodynamic relations can be deduced by it. For example, Helmholtz free energy F as a function of specific volume v and temperature T of the system is a complete EOS. Unfortunately, the concrete expressions of these complete EOSs are unavailable. Here we establish a practical form of the complete EOS based on the pressure function pT(v) and constant-volume specific heat function Cv(v，T) This complete EOS is mathematically equivalent to the Helmholtz free energy F. Here pT(v) is determined by the measurement and Cv(v，T) can be expressed by two parts. One part is the lattice contribution based on the Debye model and the other part is electronic contribution obtained from the free electron model. Using this complete EOS we calculate the isothermal equation for six metals from the Hugoniot data. Good agreement between the isothermal equation and the experimental data verifies the reliability of the complete EOS. Through this complete EOS we can derive the concrete expression of physical parameters, and these physical parameters including the volume expansion coefficient, the volume speed of sound, the adiabatic modulus, and W-J coefficient are calculated by using the experimental data of Cu. Analyzing their variation trends we can timely adjust parameter in the calculation of the EOS. This kind of complete EOS is useful in the field of high temperature and high pressure physics.
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Keywords:
- specific heat /
- complete equation of state /
- thermodynamic quantity
[1] Jing F Q 1999 Introduction to Experimental Equation of State(2nd Ed.) (Beijing:Science Press) p398(in Chinese)[经福谦1999实验物态方程导引(第二版)(北京:科学出版社)第398页]
[2] Chen J X, Jin K, Wu Q 2014 Chin. J. High Pres. Phys. 28 293 (in Chinese)[陈俊祥, 金柯, 吴强2014高压 28 293]
[3] Chen J X, Yu J D, Li P, He H L 2015 Acta Phys. Sin. 64 086401 (in Chinese)[陈俊祥, 于继东, 李平, 贺红亮2015 64 086401]
[4] Anderson O L 2000 Geophys. J. Int. 143 279
[5] Wu Q 2004 Ph. D. Dissertation (Mianyang:China Acedemy of Engineering Physics) (in Chinese)[吴强2004博士学位论文(绵阳:中国工程物理研究院)]
[6] Song P, Cai L C 2009 Acta Phys. Sin. 58 1879 (in Chinese)[宋萍, 蔡灵仓2009 58 1879]
[7] Zhang D, Sun J X 2012 Chin. Phys. B 21 080508
[8] Zhai D, Wei Z, Feng Z F, Shao X H, Zhang P 2014 Acta Phys. Sin. 63 206501 (in Chinese)[翟东, 韦昭, 冯志芳, 邵晓红, 张平2014 63 206501]
[9] Chen J X 2012 Appl. Phys. 2 77 (in Chinese)[陈俊祥2012应用物理2 77]
[10] Xu X S, Zhang W X 1986 Introduction to Practical Equation of State(Beijing:Science Press) p292(in Chinese)[徐锡申, 张万箱1985实用物态方程理论导引(北京:科学出版社)第292页]
[11] Agnes D, Paul L, and Mohamed M 2004 Phys. Rev. B 70 094112
[12] Marsh S P 1980 LASL Shock H goniot Data (Berkeley American:University of California Press) p57
[13] Mitchell A C, Nellis W J 1981 J. Appl. Phys. 52 3363
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[1] Jing F Q 1999 Introduction to Experimental Equation of State(2nd Ed.) (Beijing:Science Press) p398(in Chinese)[经福谦1999实验物态方程导引(第二版)(北京:科学出版社)第398页]
[2] Chen J X, Jin K, Wu Q 2014 Chin. J. High Pres. Phys. 28 293 (in Chinese)[陈俊祥, 金柯, 吴强2014高压 28 293]
[3] Chen J X, Yu J D, Li P, He H L 2015 Acta Phys. Sin. 64 086401 (in Chinese)[陈俊祥, 于继东, 李平, 贺红亮2015 64 086401]
[4] Anderson O L 2000 Geophys. J. Int. 143 279
[5] Wu Q 2004 Ph. D. Dissertation (Mianyang:China Acedemy of Engineering Physics) (in Chinese)[吴强2004博士学位论文(绵阳:中国工程物理研究院)]
[6] Song P, Cai L C 2009 Acta Phys. Sin. 58 1879 (in Chinese)[宋萍, 蔡灵仓2009 58 1879]
[7] Zhang D, Sun J X 2012 Chin. Phys. B 21 080508
[8] Zhai D, Wei Z, Feng Z F, Shao X H, Zhang P 2014 Acta Phys. Sin. 63 206501 (in Chinese)[翟东, 韦昭, 冯志芳, 邵晓红, 张平2014 63 206501]
[9] Chen J X 2012 Appl. Phys. 2 77 (in Chinese)[陈俊祥2012应用物理2 77]
[10] Xu X S, Zhang W X 1986 Introduction to Practical Equation of State(Beijing:Science Press) p292(in Chinese)[徐锡申, 张万箱1985实用物态方程理论导引(北京:科学出版社)第292页]
[11] Agnes D, Paul L, and Mohamed M 2004 Phys. Rev. B 70 094112
[12] Marsh S P 1980 LASL Shock H goniot Data (Berkeley American:University of California Press) p57
[13] Mitchell A C, Nellis W J 1981 J. Appl. Phys. 52 3363
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