# T-S Carnot Cycle for Photon Gas

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1. Dec 28, 2014

### repetelww

So I have been thinking about the photon gas, and I have read several papers talking about how a Carnot cycle could be created for it. This is fantastic, and it is something I am quite comfortable with. All of the papers present the P-V diagram as the "golden" Carnot cycle for the photon gas, and say that the construction of a T-S diagram would be "trivial", but do not present what the cycle would actually look like, and I have searched/read for quite some time, but have not been able to come up with definitively what it should look like.

Would it differ from the one presented for the ideal gas? Such as
http://en.wikipedia.org/wiki/Carnot_cycle#The_temperature-entropy_diagram

I apologize if this is something trivial to you, but it bothers me since P does not depend on V, and that P and T are not independent in the photon gas. It seems like such a diagram would be more convoluted than the one presented for an ideal gas.

2. Dec 28, 2014

### WannabeNewton

See the attachment (Kardar "Statistical Physics of Particles" problem 1.10).

#### Attached Files:

• ###### photon gas carnot cycle.png
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3. Dec 29, 2014

### repetelww

This is a nifty little problem set, and it very nicely demonstrates some of the key ideas of the photon gas. It is a great representation of the P-V plane for the Carnot Cycle. I have no difficultly in accepting any of the information required for the construction of the P-V plane. The issue become when I attempt to construct the T-S plane for the photon gas.

Essentially, I know the typical construction for such a T-S plane for say an ideal gas, would require the use of isobaric and isentropic processes. But when I think about the isobaric processes in particular for the photon gas, since the P and T are not independent, it appears that have constant pressure requires constant temperature, so that any isobaric processes would not actually change the temperature. So in my mind the plot in the T-S is just a straight line for the Carnot Cycle with a photon gas.