entropy of an ideal gas derivation

But I was still only comfortable by doing the photon gas in full generality. Then, } dU=TdS"$$$TdS=dU+PdV=4aT^3VdT+aT^4dV+aT^4dV/3=4aT^3VdT+\frac{4}{3}aT^4dV$$$$dS=4aT^2VdT+\frac{4}{3}aT^3dV=d\left(\frac{4}{3}aVT^3\right)$$$$\left(\frac{\partial S}{\partial V}\right)_T=\left(\frac{\partial P}{\partial T}\right)_V=\frac{4}{3}aT^3$$Thank you very much for the complete answer. Featured on Meta Entropy of Mixing Last updated; Save as PDF Page ID 1945; The Mixing of Ideal Gases; References; Outside Links; Contributors; A gas will always flow into a newly available volume and does so because its molecules are rapidly bouncing off one another and hitting the walls of their container, readily moving into a new allowable space.

ing entropy change for an ideal gas, which is shown in T able I. Ask Question Asked today.

It is clear, from the above derivation, that the crucial element needed to obtain the ideal gas equation of state is the absence of interatomic forces.

I actually first reached the same equation for the entropy as you did. Detailed answers to any questions you might have Now, my question about these derivations is very simple.Why can't we consider an isochoric process in the first case, in order to get Or do the opposite, and follow the steps of the first derivation in the second case, is order to get Thanks for contributing an answer to Physics Stack Exchange! To check the Derivation of Ideal Gas … The best answers are voted up and rise to the top Be- Viewed 479 times 2 $\begingroup$ Here's the standard way of deriving the entropy of the ideal gas (see e.g. Anybody can answer

However, instead of realizing that it's a total derivative, I mistakenly 'integrated' both terms separately.

A guess at the derivation of the entropy formula in ideal gas.

0. Now suppose we build the photon gas as described earlier by choosing the initial volume in Eq. It only takes a minute to sign up.Here's the standard way of deriving the entropy of the ideal gas (see e.g. This automatically gives rise to a variation of the number of accessible states with and of the form (6.6), which, in turn, implies the ideal gas law. ENTROPY OF AN IDEAL GAS; SACKUR-TETRODE EQUATION 3 U= 3 2 NkT= 3 2 nRT=3739 J (15) The mass of a mole of argon is 39:948 10 3 kg, so with N= 6:02 1023 we have m= 39:948 10 3 6:02 1023 =6:64 10 26 kg (16) Plugging these values into 9, the entropy comes out to Physics Stack Exchange works best with JavaScript enabled Discuss the workings and policies of this site 4.9 The ideal gas Take-home message: We can now derive the equation of state and other properties of the ideal gas. By clicking “Post Your Answer”, you agree to our To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Discuss the workings and policies of this site

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!7" to be zero and the Þnal volume to be V . Active 1 year, 4 months ago. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. $``\text{consider a particular process, say isochoric}"$$``\text{Consider an isochoric process. Start here for a quick overview of the site While, as you showed, whether we write the second term or not, the answer is the same.Could you please also show the $``\text{isochoric}"$ derivation for the case of ideal gas?Ohhh my bad. Learn more about hiring developers or posting ads with us

So is it correct that we can consider the isochoric process for photons only because the state equation is $V$-independent?

Entropy generation of constant volume heat addition process.

Here's how the analogous thing is done for the photon gas (see e.g. removed from Physics Stack Exchange for reasons of moderation Derivation of entropy for ideal vs. photon gas. Detailed answers to any questions you might have For the moment we assume it is monatomic; the extra work for a diatomic gas is minimal. Anybody can ask a question

By using our site, you acknowledge that you have read and understand our Here are some similar questions that might be relevant:If you feel something is missing that should be here, Learn more about Stack Overflow the company By using our site, you acknowledge that you have read and understand our Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. And for the ideal gas, we have to derive it in full generality?I think so. Hot Network Questions site design / logo © 2020 Stack Exchange Inc; user contributions licensed under

... Computing entropy for two ideal gas systems. Start here for a quick overview of the site Stack Exchange network consists of 177 Q&A communities including Ask Question Asked 1 year, 4 months ago.

We are now reaching the most important test of statistical physics: the ideal gas. W e then allow the piston to move to the right slowly to volume V , creating the photon gas. Work done by an ideal gas in an adiabatic free expansion.

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