First slide

Law of equipartition of energy

Question

The specific heats, $C_{P}$ and $C_{v}$ of gas of diatomic molecules, A, is given (in units of J $m o l^{- 1} K^{- 1}$ by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then

Moderate

A

A has a vibrational mode but B has none
B

A has one vibrational mode and B has two.
C

A is rigid but B has a vibrational mode.
D

Both A and B have a vibrational mode each

Solution

For any ideal gas $γ = \frac{C_{p}}{C_{v}} = 1 + \frac{2}{f}$
For the first case A $\frac{29}{22} = 1 + \frac{2}{f}$
Solving for f we get f= 44/7= 6
So it has 3 translational , 2 rotational and 1 vibrational degrees of freedom
For the second case B solving for f we get f= 14/3 = 5
so it has 3 translational and 2 rotational degrees of freedom

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