The heat capacity of an object describes how much heat is required to change its temperature. Because heat is a path function, the heat capacity at constant volume is different than the heat capacity at constant pressure.
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Cp for real gases is expressed as power series which has the form Cp= a+bT+c/T². Which type of power series it is? 3rd term is confusing for me. Moreover, it is also expressed like Cp= a+bT+cT². What is the difference between the two forms?
I wouldn't worry too much about the name, or type, of the power series. The 1/T² term is just there because it helps in describing the empirical Cₚ(T) data. For empirical equations like this, all that matters is how well the equation can describe the data. A common equation used to describe Cₚ(T) uses not only a quadratic (T²) and an inverse quadratic term (T⁻²) but also a cubic term (T³). This one is common enough that it does have a name: the Shomate equation. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Oc_iOWhZGVQ.html
Yes, that's essentially right. More precisely: a diatomic (or triatomic, polyatomic) molecule **does** still behave like a 3D PIB, but it's only the translational KE of the molecule that is described by the 3D PIB model. Its vibrational and rotational energy and heat capacity are not captured by the 3D PIB model. In the context of this video, you're absolutely correct: U = 3/2 nRT and H = 5/2 nRT are only correct for monatomic ideal gases.
