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*From*: carmelo@pacific.net.sg*Date*: Fri, 22 Jun 2007 10:08:03 +0800

Quoting John Denker <jsd@av8n.com>:

Feynman is applying thermodynamics to photons and has chosen

to treat T and V as independent variables and to treat U(T,V) and P(T,V)

as dependent variables.

He takes the partial derivative of U=3PV (comes

from equation 39.17) holding T constant and obtains:

dU/dV (const T) = 3P

I was expecting:

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

Actually, Feynman was using

PV = (gamma – 1)U (39.11)

and

dU = (PdV + V dP) / (gamma – 1) (39.12)

and deduce that

PV^gamma = C (39.14)

I don’t see any problem with Feynman’s calculations.

Feynman’s conclusion was on the compressibility of radiation. He related this to the contribution of radiation pressure in the stars. However, the compressibility of radiation may have significant impact on the attenuation of photons’ energy from distant stars or supernova! That is, the light may get “tired” because the vacuum in space is not perfectly empty; it is filled with background cosmic radiations.

One possible experiment is to illuminate a tunnel say, in a linear collider, by using lights with different wavelengths and intensities. By aiming a laser light through the tunnel with “large number of photons”, we may verify the attenuation and fine-tune Hubble’s Law. We may discover that the universe is not expanding so fast too. Whether Einstein’s profound mistake in the cosmological term, is really profound, it is still too early to tell.

Alphonsus

**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>

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