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In consequence the specific heat of polyatomic gases may often be regarded as approximately constant over fairly wide intervals of temperature.
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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.
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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.