Phenomenological Derivation of the Ideal Gas Equation

While mathematical theory often mns roughly parallel to physical science, sometimes faster and other times slower, a key strategy is a process called the phenomenological approach. In this method a process is studied to determine the variables on which it depends and then an equation is developed, which matches the results of the problem. Often it requires a number of data points to determine whether the result is linear, quadratic, or some higher order in a given variable but the case of the ideal gas law is an excellent starting point to illustrate this method and at the same time enter the important domain of thermodynamics. 

Although we could digress to mention early concepts of science by ancient Greek philosophers, we will begin with the first attempts at quantitative studies that can be related with mathematical 

FIGURE 1.2 A schematic of the J-tube Sir Robert Boyle used to study the PV relationship. 

Spring of Air, and its Effects The data in Table 1.1 lead to an important phenomenological 

Here Ci is the first constant in this study. We should note that Boyle s experiments were carried out at essentially constant room temperature but do we know that temperature has an effect Not liom this data. 

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