Information hidden in the state change of a gas obtained from the theoretical integrations of the partial derivatives

The calculations of the change in the gas state are critical in most engineering applications. Generally, engineers and scientists use Boyle-Charles-Gay Lussac's (B-C-G) law of P1V1/T1 = P2V2/T2 to calculate pressure (P), volume (V), and temperature (T) of gases and vapors. Although the B-C-G law provides accurate gas properties of P-V-T, it does not give any specific information about the process of a state change by which gases and vapors change their state. In this study, the authors performed, for the first time, the theoretical integrations of the partial derivatives obtained from the differentiation of the B-C-G law. The findings from this study were thoroughly compared with experimental data. It was verified that the integration methods proposed in this study provided the detailed analysis on the differential properties of ΔP, ΔV, and ΔT accurately. Furthermore, the stepwise analysis of the integration of the partial derivatives revealed that the state changes of gases inherently involve energy loss, which can be defined as the efficiency. In other words, this study demonstrated that the state changes of all matters include energy loss, and it is a natural phenomenon. Therefore, it can be said that this study suggests the theoretical method to select the most efficient process for the state change of a material.