Coronal mass ejections (CMEs) are the most energetic eruptive phenomenon occurring in the Sun's atmosphere and the major driver of space weather. They carry a huge amount of mass, kinetic energy and magnetic flux into the interplanetary space, and therefore may cause many significant consequences in the geospace. In this paper, we develop a generic flux rope model to infer three physical parameters of CMEs as well as their variations with heliocentric distance through the usage of the latest STEREO (Solar TErrestrial RElations Observatory) observations. The first parameter, is the polytropic index, Γ, that describes the thermodynamic process of the gas, and the other two are the Lorentz force and the thermal pressure force, that reveal the internal cause of the CME expansion.
 CMEs have been observed and studied for decades. There have been many observations, either through remote sensing observations or in situ samplings, revealing the internal properties of CME plasmas. For example, the remote sensing data from SOHO/UVCS (ultraviolet coronagraph spectrometers [Kohl et al., 2006]) can diagnose the plasma temperature, density, velocity and heating at a few solar radii from the Sun. Such spectroscopic analyses suggested that CMEs be a loop-like structure [e.g., Ciaravella et al., 2003] with helical magnetic field [e.g., Antonucci et al., 1997; Ciaravella et al., 2000], and probably have a higher temperature than that in the typical Corona in the near Sun region [Ciaravella et al., 2003]. The thermal energy deposited into CME plasmas is roughly comparable to the kinetic and gravitational potential energies of CMEs in the inner corona [e.g., Akmal et al., 2001; Ciaravella et al., 2001]. Some Internal properties of CMEs can also be revealed from in situ observations, e.g., by Ulysses and ACE spacecraft. For example, the interplanetary CMEs (ICMEs) at 1 AU usually show a lower temperature and stronger magnetic fields than that in the ambient solar wind [e.g., Burlaga et al., 1981; Richardson and Cane, 1995; Farrugia et al., 1993]. The ion charge states in ICMEs are often higher [e.g., Lepri et al., 2001; Lynch et al., 2003]. Based on the analysis of ion charge states, it was also found that the thermal energy input to the CME plasmas is at the same order of the CME kinetic energy [e.g., Rakowski et al., 2007].
 The above studies provided the information of the internal properties of CMEs, but only at a certain position and/or at a certain time. What is largely lacking is the global observations and thus the global understanding of the evolution of the internal state of CMEs during their continuous propagation throughout the interplanetary medium. What thermodynamic process does the CME plasma undergo? What happens with the various forces involved? Limited knowledge on these global issues were obtained through indirect ways, largely from the statistical combination of observations of many CMEs from multiple spacecraft over a long time period. The multiple-spacecraft measurements suggested that the polytropic index of CME plasmas be below 1.3 [e.g., Liu et al., 2006], which is apparently different from that of solar wind, which is about 1.46 [Totten et al., 1995]. The radial widths of CMEs continuously increase at the order of local Alfvén speed as they move away from the Sun within 10 AU [e.g., Wang and Richardson, 2004; Wang et al., 2005; Jian et al., 2008], and the magnetic field decreases faster in ICMEs than in ambient solar wind but the temperature does not [e.g., Wang and Richardson, 2004; Wang et al., 2005; Liu et al., 2006]. It should be noted that all the above conclusions were established on statistical surveys, which cannot review the detailed evolution behavior of any individual CMEs.
 It is now well accepted that CMEs, at least a significant percentage of them, have a flux rope-like structure (Figure 1). Thus we try to study the internal state of CMEs by establishing a flux rope model. There are already various flux rope models concerning CME initiation and/or propagation [e.g., Burlaga et al., 1981; Goldstein, 1983; Chen, 1989; Forbes and Isenberg, 1991; Kumar and Rust, 1996; Vandas et al., 1997; Gibson and Low, 1998; Titov and Démoulin, 1999]. These models have their own specific purposes, and may not suit the issues attacked in this paper. We present our model in the next section. We then make a case study in section 3 by applying the model to the CME that occurred on 8 October 2007, whose expansion and propagation over a large distance throughout the interplanetary space were well observed. In section 4, a brief summary is given. Finally, we thoroughly discuss the limitations and approximations of the model in section 5.