## 1 Introduction
[21] used CO and C\({}_{2}\)H\({}_{4}\) as the main indicators and C\({}_{2}\)H\({}_{6}\) and C\({}_{2}\)H\({}_{4}\)/C\({}_{2}\)H\({}_{6}\) as auxiliary indicators to divide the stages of spontaneous combustion. [PERSON] et al. [22] pointed out that C\({}_{2}\)H\({}_{6}\) and temperature have poor regularity, with the appearance of C\({}_{3}\)H\({}_{8}\) at high temperatures, and neither of them are suitable gas warning indicators in the low-temperature stage of spontaneous combustion. [PERSON] et al. [23] eliminated the error caused by the different initial concentrations of the index gas at different locations by introducing the K value. [PERSON] et al. [24] divided the spontaneous combustion of coal into seven stages, using six characteristic temperatures, and provided the gas index and threshold values corresponding to each characteristic temperature. Based on the original analysis of indicator gas concentrations and ratios, [PERSON] et al. [25] introduced the growth rate of the indicator gas to optimize predictors. The above research reveals the law and mechanism of the primary oxidation and secondary oxidation of coal with respect to its spontaneous combustion, as well as a variety of gas warning indexes and systems. Moreover, it is well known that old goals often have gas exchanges with new goafs [26; 27; 28; 29]. The gases produced in the secondary oxidation process are the same type as those produced in primary oxidation, which will affect the concentration of the original gas field in the mining area and result in a judgment deviation of the severity of the spontaneous combustion of coal in the goat from the coal seam in question. Currently, the early warning indicators and critical values of the spontaneous combustion of coal are generally determined by collecting fresh coal samples at the working face and then carrying out temperature-programming experiments in a laboratory, which are used to guide the work regarding the development of an early warning system for the spontaneous combustion of coal at a coal mine site. This has important guiding significance for warning systems for the spontaneous combustion of coal and oxidation in separate goat that have not been connected with an old goat [30; 31]. However, whether the gas produced by the secondary oxidation of the old goat will affect the corresponding relationship between the early warning value and the temperature of the goat being mined still requires further research to be determined. In this study, secondary oxidation experiments of oxidized coal from three coal mines were carried out using a coal oxidation and temperature rise experimental system. Thus, the gas generation law and its corresponding relationship with temperature are analyzed herein. The influence of the second oxidized gas entering the goat on the gas early warning index is discussed, while the existing gas early warning index is optimized and corrected. Ultimately, this study provides new ideas to be applied in early warning systems for the spontaneous combustion of coal gas and for the improvement of the accuracy of early warning systems and the scope of their application so as to guide the effective prevention and control of the spontaneous combustion of coal in underground coal mining.