We may mention the possibility of a curious change from vibration to rotation, an instance of which is afforded by the ethane molecule C 2H 6. In consequence the specific heat of polyatomic gases may often be regarded as approximately constant over fairly wide intervals of temperature. As the temperature increases, the various normal modes successively contribute to the specific heat. The various frequencies ω α for a polyatomic molecule generally range over a very wide interval.
In practice, however, this limit is not reached, since polyatomic molecules usually decompose at considerably lower temperatures. The distance a is just the coordinate x C of the oxygen atom laying on y′ axis it can be found according eq. One can find the MI relative the axis z′ as a sum of two MI of MP being at the distance d from the z′ axis I z′ = 2 m 1 d 2. The required MI is I z,C = I z ′ – ma 2*, where a is a distance between two parallel z axes. To find the molecule MI we shall take advantage of the theorem on parallel axis (see (1.3.48)): I z′ = I z ,C + ma 2, where I z′ is the MI of the molecule relative axis z′, passing through an oxygen atom and parallel to the axis z. We direct an axis z upwards perpendicular to a molecule planes.
The origin (intersection of three axes C) is superimposed with the molecule CM. Calculate first the MI I z of the water molecule relative to an axis z′ which passes through oxygen atom perpendicular to a molecule plane. A water molecule consists of three MPs (nuclei of atoms) with a total mass m = 2 m 1 + m 2, where m 1 and m 2 are masses of hydrogen and oxygen atoms, respectively. Solution: Let's arrange a molecule as it is represented in Figure E1.13.
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