Question

Given the molar specific heat cv of a gas at constant volume, you can determine the number of degrees of freedom s that are energetically accessible. for example, at room temperature cis-2-butene, c4h8, has molar specific heat cv=70.6jmol⋅k. how many degrees of freedom of cis-2-butene are energetically accessible?

Answer 1

The molar specific heat Cv = R s / 2
70.6 J/mol.K = (8.314 J/mol.K) * s / 2
So the number of degrees of freedom are:
s = 16.98 = 17

Answer 2

The correct answer is 17

The explanation:

To get how many degrees of freedom of Cis-2-butene we are going to use this formula of the molar specific heat:

Cv = R.s / 2

when Cv is the molar specific heat = 70.6 J/mol.K

and R is the ideal gas constant = 8.314 J/mol.K

and S is the degrees of freedom of cis-2-butene : it is the number of independent coordinates to specify the motion of a molecule.

so by substitution:

70.6 J/mol.K = [8.314 J/mol.K] * s / 2

So, the number of degrees of freedom = s = 16.98 ≈ 17