Specific heat of a monotomic gas

[Apashanka]

Homework Statement

The problem is attached below

Relevant Equations

The problem is attached below

Given this problem I have calculated the partition function as $$z=1+e^{-\beta E_1}$$
And calculated the average internal energy as $$<U>=\frac{E_1 e^{-\beta E_1}}{1+e^{-\beta E_1}}$$
And thereafter taking the partial derivative of <E> with respect to temp. T the specific heat obtained is option (b)...
Am I correct??

 

[ehild]

Homework Statement:: The problem is attached below
Relevant Equations:: The problem is attached below

View attachment 258085
Given this problem I have calculated the partition function as $$z=1+e^{-\beta E_1}$$
And calculated the average internal energy as $$<U>=\frac{E_1 e^{-\beta E_1}}{1+e^{-\beta E_1}}$$
And thereafter taking the partial derivative of <E> with respect to temp. T the specific heat obtained is option (b)...
Am I correct??

It looks good.
See @mjc123's post.

 

[mjc123]

That deals with the electronic energy of the atoms. What other energy do they have?

 

[ehild]

That deals with the electronic energy of the atoms. What other energy do they have?

Yo are right. I did not notice that it was a monoatomic gas.

 

[Apashanka]

That deals with the electronic energy of the atoms. What other energy do they have?

Then what should be the answer

 

[mjc123]

Then what should be the answer

Working that out is your job.

 

[Apashanka]

Working that out is your job.

Actually I need some help regarding this...one part I have got but how to get the next part..,can you suggest something??

 

[DrClaude]

When you have independent degrees of freedom, the energy is a sum of terms for the different degrees of freedom. For example, you usually have for a diatomic gas molecule
$$
E_\mathrm{total} = E_\mathrm{translation} + E_\mathrm{rotation}.
$$
The separability applies also to the averages,
$$
\langle E_\mathrm{total} \rangle = \langle E_\mathrm{translation}\rangle + \langle E_\mathrm{rotation} \rangle.
$$