Chronology |
Current Month |
Current Thread |
Current Date |

[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |

*From*: John Denker <jsd@av8n.com>*Date*: Sun, 17 Jun 2007 23:58:46 -0400

On 06/17/2007 10:33 PM, Jeffrey Schnick wrote:

....

Thanks for your informative response. I perceive the scaling argument

to be elegant and powerful. At present, however, I don't follow it in

this case. I assume the equation to which you refer when you write "you

can't have an extensive variable on one side of the equation and not the

other" is:

(1) dU/dV (const T) = 3P + 3V dP/dV (const T)

On the left is the ratio of a change in an extensive variable to a

change in an extensive variable. That ratio is an intensive variable.

The first term on the right is clearly an intensive variable. The

second term on the right is an extensive variable times the ratio of a

change in an intensive variable to a change in an extensive variable.

The ratio is a reciprocal extensive variable. The product of the

extensive variable 3V times that reciprocal extensive variable is thus

an intensive variable. As such, every term in equation (1) scales like

the zeroth power of the size of the system and we can't use the scaling

argument to establish the fact that the second term on the right must

vanish.

That argument is a correct non-proof. It says that a

certain line of reasoning fails to prove that the pressure

is independent of volume, under black-body conditions.

But the door remains open to other lines of reasoning.

In particular, consider a piston between two boxes of black-body

radiation. Both boxes are at temperature T. One box is larger

than the other. My physical intuition tells me that to a very

good approximation (for a wide range of reasonable sizes and

temperatures), the black-body radiation pressure is the same on

both sides of the piston.

There are so many physical arguments supporting this intuition

that I hardly know where to start. One argument uses the same

apparatus as the Gibbs "paradox" experiment, i.e. a box with

photon gas on both sides of a partition, and then we pull out

the partition. Neglecting very small effects (Casimir-like

effects etc.) we now have one big box of photons, instead of

two small boxes, and the photon pressure is unchanged. For me

this is very graphic, very pictorial: I visualize the photon

modes in the box ... and most of the energy is in modes that

are negligibly affected by the partition.

Another argument is that I know the black-body radiation brightness

formula, and it doesn't have a V in it ... but that is slightly

cheating, because Feynman was starting to /derive/ the blackbody

formula, and he didn't want to make a circular argument.

Anyway, my advice is don't obsess over equation (1). Think about

the underlying physics.

(Also, as mentioned in my previous note, beware of negative

transference from your experience with a gas of ordinary

molecules. Black-body conditions != constant-N conditions.)

**References**:**[Phys-l] thermo differential and extensive/intensive variables***From:*Stefan Jeglinski <jeglin@4pi.com>

**Re: [Phys-l] thermo differential and extensive/intensive variables***From:*John Denker <jsd@av8n.com>

**Re: [Phys-l] thermo differential and extensive/intensive variables***From:*Stefan Jeglinski <jeglin@4pi.com>

**Re: [Phys-l] thermo differential and extensive/intensive variables***From:*John Denker <jsd@av8n.com>

**Re: [Phys-l] thermo differential and extensive/intensive variables***From:*Stefan Jeglinski <jeglin@4pi.com>

**[Phys-l] Photon Thermodynamics***From:*"Jeffrey Schnick" <JSchnick@Anselm.Edu>

**Re: [Phys-l] Photon Thermodynamics***From:*John Denker <jsd@av8n.com>

**Re: [Phys-l] Photon Thermodynamics***From:*"Jeffrey Schnick" <JSchnick@Anselm.Edu>

- Prev by Date:
**Re: [Phys-l] Photon Thermodynamics** - Next by Date:
**[Phys-l] POSITIVE AND NEGATIVE ENERGY SYMMTERY AND INDUCED GRAVITY PT1** - Previous by thread:
**Re: [Phys-l] Photon Thermodynamics** - Next by thread:
**Re: [Phys-l] Photon Thermodynamics** - Index(es):