Calculations of The Change of State of a Gas By Integrating The Partial Derivatives

It will not be denied that the calculations of the change of state for a gas is highly important in most engineering applications. For determining the gas’s properties such as the pressure ( P ), the volume ( V ) and the temperature ( T ), engineers and scientists uses the Boyle’s, Charles’s and Gay-Lussac’s (B-C-G) law of P 1 V 1 / T 1 = P 2 V 2 / T 2 . Although the B-C-G law provides the accurate property values of a gas, it give no detailed information embedded in the process when a gas changes its state. In this study, the author theoretically carried out the integrations of the partial differentials when differentiating the B-C-G law, which has not been tried by anyone up to now. The integration results of this study were thoroughly compared with the experimentally measured data and it was confirmed that the integration methods suggested in this study accurately provides the differential properties on ΔP , ΔV and ΔT . In addition to it, through the stepwise analysis of the integration of the partial differentials, it revealed that the efficiency in the change of state of a gas inherently exists higher than the Carnot cycle, which is operating between the same conditions. Therefore, the results of this study can be lead to the conclusion that all changes of state of all materials inevitably accompanies an energy loss and it is a natural phenomenon.