How to Estimate Internal Energy and Heat Capacity Without Partition Functions?

[MyNewPony]

Homework Statement

a) Estimate the internal energy E in the high temperature (equipartition) limit for CO.
b) Estimate the heat capacity Cv in the high temperature (equipartition) limit for NH3.

Do not use partition functions in your calculations.

Homework Equations

<E> = KbT
Cv = (7/2)R

The Attempt at a Solution

a) According to the equipartition theorem, <E> = KbT at the high temperature limit. How are we suppose to calculate <E> without a given temperature?

b) According to the equipartition theorem, Cv = (7/2)R at the high temperature limit. Then, (7/2)R = 29.099 J/mol*K. Is this correct?

 

[mark726]

a) Without a given temperature, it is not possible to calculate the internal energy <E> for CO in the high temperature limit using the equipartition theorem. The equation <E> = KbT only applies at a specific temperature. Without that information, it is not possible to estimate the internal energy.

b) Your calculation for the heat capacity Cv for NH3 in the high temperature limit is correct. At high temperatures, the equipartition theorem predicts that the heat capacity will approach (7/2)R, where R is the gas constant. This value is approximately 29.099 J/mol*K.