Thermodynamics and Thermochemistry - Result Question 67
####67. $C _V$ value of He is always $\frac{3 R}{2}$ but $C _V$ value of $H _2$ is $\frac{3 R}{2}$ at low temperature and $\frac{5 R}{2}$ at moderate temperature and more than $\frac{5 R}{2}$ at higher temperature. Explain in two or three lines.
(2003, 2M)
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Solution:
- He is monatomic, so it has only three degree of freedom (translational only) at all temperature hence, $C _V$ value is always $\frac{3}{2} R$.
Hydrogen molecule is diatomic, has three translational, two rotational and one vibrational degree of freedom. The energy spacing between adjacent levels are in the order of :
$$ \text { translational }<\text { rotational }<\text { vibrational } $$
At lower temperature only translational degree of freedom contribute to heat capacity while at higher temperature rotational and vibrational degree of freedom starts contributing to heat capacity.
