INTRODUCTION
The research of equation of state (EOS) has always been an important field in chemical engineering thermodynamics. In general, EOS can be divided into the specific EOS for a given substance and the general EOS for many kinds of substances1-3. Differently, the latter always has a wider range of applications while the precision is less than the former. Fortunately, some multi-parameter EOSs both possess a high calculation precision and a wide range of applications4,5, although their solution methods with unknown multiple-parameters are always very difficult and time-consuming. Among the large number of multi-parameter EOSs, the Benedict-Webb-Rubin6-8 EOS (B-W-R EOS) and the Martin-Hou EOS (M-H EOS)9-12 are very representative and excellent with significant differences in terms of the precision and the range of application. On the one hand, the calculation precision of the two equation in gas-phase state is approximately equivalent and high enough for the practical application while the B-W-R EOS is more precise in liquid-phase state; On the other hand, the M-H EOS has a much broader scope of applications for most kinds of substances, even the strong polar substances such as H2O and NH3 and so on, while the B-W-R EOS is mainly used to calculate the properties of hydrocarbons. Moreover, the initial value conditions for the derivation of the unknown characteristic constants in the M-H EOS are more accessible and easy to use.
Although the M-H EOS was originally put forward in the form of an empirical equation, its theoretical formula had been strictly proved13,14by the theory of Hard-particle Perturbation theory15-18. Nowadays, the main investigation of the M-H EOS has changed from the theory’s exploration to the application of given substances in different cases. First and foremost, especially in refrigeration industry19-21, the M-H EOS is widely applied as a specific EOS for a given substance, such as H2O22, 23, CO224, natural gas25and so on26. Second, the M-H EOS is extended to achieve diversified applications27-32, e.g., the crossover multi-parameter EOS31, 32. Last but not least, the combination of the M-H EOS with other theories is further developed, which has solved many thorny problems in the past33-36.
Although many satisfying researches have been achieved, the improvement of the M-H EOS itself is essentially stagnant for the application in liquid-phase state after the modified M-H EOS put forward by Hou12. In fact, the original M-H EOS is not very proper to the calculation in liquid-phase state9, as the improved formula, Hou’s modified M-H EOS is also not as satisfactory as desired in term of the calculation precision. In general, most average deviation by Hou’s modified M-H EOS is less than 5% in liquid-phase state, while partial maximum deviations are up to 15%~20%12. It is still of great potential to improve the calculation precision of the M-H EOS in liquid-phase state.
In this work, we focus on improving the precision of the M-H EOS in liquid-phase state. First, based on rigorous derivation and a large number of literature data analysis, the M-H EOS is further modified and the novel formula will be put forward by introducing an appropriate revision factor h ; And then, the novel M-H EOS will be applied to six representative substances to verify the generality of the novel EOS and the improvement of calculation precision in liquid-phase state, all the data calculated by different EOS are listed in the supporting information. At last, the conclusion is drawn. In the appendixes, the unknown characteristic constants in the novel M-H EOS are derived in detail.