Some Equations of State for Pure Gases

SOME EQUATIONS OF STATE FOR PURE GASES 16.2.1. Ideal Gas 

This is interesting because Mv /2 is kinetic energy. Temperature is a measure of molecular motion or kinetic energy, Mv /2 oc T) and if we write this proportionality as 

This is at fixed volume because we are considering a specific container of gas. 

The relationship between C, and Cp can be seen by using Table 2.1 to derive an expression for dU/dT)y, which is C. This turns out to be 

In other words, the heat capacities Cv and Cp are constants for ideal gases. This takes us quickly into the worlds of statistical mechanics and the kinetic theory of gases, but also raises several points of direct thermodynamic interest. First, (16,4) and (16.5) apply only to monatomic ideal gases these can move independently (or have three degrees of translational freedom) along each of the three orthogonal axes. 

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