Legal. = Otherwise, it varies. {\displaystyle v} The table below essentially simplifies the ideal gas equation for a particular processes, thus making this equation easier to solve using numerical methods. Since the ideal gas law neglects both molecular size and intermolecular attractions, it is most accurate for monatomic gases at high temperatures and low pressures. {\displaystyle f(v)\,dv} In reality, there is no such thing as an ideal gas, but an ideal gas is a useful conceptual model that allows us to understand how gases respond to changing conditions. {\displaystyle T} Then the time-averaged kinetic energy of the particle is: where the first equality is Newton's second law, and the second line uses Hamilton's equations and the equipartition theorem. {\displaystyle {\bar {R}}} In Example \(\PageIndex{1}\) and Example \(\PageIndex{2}\), two of the four parameters (P, V, T, and n) were fixed while one was allowed to vary, and we were interested in the effect on the value of the fourth. 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