Degrees of freedom - molecule of water vapor

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In solid form, water (H2O) has six degrees of freedom, consisting of three translational and three vibrational due to bond potential energy. When water transitions to vapor, the degrees of freedom increase significantly. In the gaseous state, each molecule has more translational freedom and additional rotational degrees of freedom, leading to a total of around 9 degrees of freedom. The phase change from solid to vapor results in a fundamental shift in molecular motion and energy distribution. Understanding these changes is crucial in thermodynamics and molecular physics.
Geronimo85
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I understand that for H20 in solid form, each atom within the molecule has 6 degrees of freedom; 3 translational and 3 due to potential energy from bonds. Does the number of degrees of freedom change when water changes phase to a vapor?
 
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Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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