Molar Specific Heat of a Gas in Terms of R & s

[doggieslover]

Part A
Using the equipartition theorem, determine the molar specific heat, C_v, of a gas in which each molecule has s degrees of freedom.
Express your answer in terms of R and s.

Okay, I know that the equipartition theorem is 1/2k_B*T

and molar specific heat is C_v= (1/n)(dU/dT)

But I don't know where to go from here, please help?

Part B

Given the molar specific heat C_v 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, \rm C_4 H_8, has molar specific heat C_v=70.6\;{\rm \frac{J}{mol \cdot K}}. How many degrees of freedom of cis-2-butene are energetically accessible?
Express your answer numerically to the nearest integer.

 

[kuruman]

But I don't know where to go from here, please help?

A monatomic molecule has three (translational) degrees of freedom and molar specific heat $C_V=\frac{3}{2}k_BT.$ Does this help?

 

[vela]

Okay, I know that the equipartition theorem is 1/2k_B*T

Your confusion arises because $\frac 12 k_{\rm B}T$ isn't the equipartition theorem. Theorems are generally statements whereas $\frac 12 k_{\rm B}T$ by itself is akin to a single word.

The principle of equipartition of energy states that each degree of freedom has, on average, an associated energy per molecule of $\frac 12 k_{\rm B}T$.