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C(v) value of He is always 3R//2 but C(v...

`C_(v)` value of He is always `3R//2` but `C_(v)` value of `H_(2)` is `3R//2` at low temperature and `5R//2` at moderate temperature and more than `5R//2` at higher temperature. Explain in two or three lines.

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The correct Answer is:
Hydrogen is diatomic so at high temperature rational and vibrational motion also counts.
Helium `(He)` gas is monoatomic and it has three translational degree of freedom. Hence, contribution of each transiational degree of freeedom towards `C_(v)` being `R//2`, so the total contribution towards `C_(v)=3xxR//2`. Hydrogen molecule is diatomic. At low temperature, rotational and vibrational contribution for `H_(2)` are zero. So, `C_(v)` for `H_(2)` at low temperature continues to be `3R//2`. At moderate temperature, rotational contribution `(=2xxR//2)` also becomes dominant and hence total contribution towards `C_(v)=(3R)/(2)+R=(5R)/(2)`. At even high temperature, vibrational contribution `(=1xxR)` also becomes significant. Hence total contibution towards `C_(v)=(3R)/(2)+R+R=(7R)/(2)`
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