Rotational contribution to heat capacity

[mhellstrom]

Hi all,

I have to determine the contribution from rotational partition function. I have determined the rotational partition function as

$$q_{rot} = \frac{T}{\omega}*(1+\frac{1}{3}(\frac{\omega}{T}+\frac{1}{15}(\frac{\omega}{T})^2+...)$$

where T >> omega and the expansion is Euler-Maclaurin. In order to find the internal energy I would like differentiate q with regard beta(kT) but I don't know ho to proceed... Any hints or advice appreciated thanks in advance.

Best
Magnus

 

[Jhero]

Hi Magnus,

Thank you for reaching out for help with your problem. Determining the contribution from the rotational partition function can be a complex task, but I will do my best to provide some guidance.

First, it's important to understand the purpose of the rotational partition function. It is used to calculate the number of energy states available to a molecule due to its rotational motion. This is important because it allows us to determine the total internal energy of the system, which is the sum of the energy from all available states.

In order to find the internal energy, you will need to integrate the rotational partition function with respect to temperature. This will give you the total internal energy of the system. However, in your case, you are trying to differentiate the partition function with respect to beta(kT). This can still be done, but it will require some additional steps.

First, you will need to convert your rotational partition function to a function of beta(kT). This can be done by using the definition of beta (β = 1/kT) and substituting it into your equation. This will give you a new equation for q_rot as a function of β.

Next, you will need to use the chain rule to differentiate the partition function with respect to β. This will give you an expression for the derivative of q_rot with respect to β. From there, you can substitute back in the definition of β to get the final expression for the derivative of q_rot with respect to temperature.

I hope this helps guide you in the right direction. If you need further assistance, don't hesitate to reach out.