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argon

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## Homework Statement

Consider a photon gas (particle-like nature) with N photons of monochromatic light in a box that has a volume V. You can assume everything is perfectly reflecting. What is the pressure of the photon gas based on the ideal gas law derivation?

## Homework Equations

N/A.

## The Attempt at a Solution

1) [itex]P=-F_{\text{on molecule}}/A[/itex]

2) [itex]F = \frac{dp}{dt}= \frac{-2h\nu}{c\Delta t}[/itex]

3) Plugging 2 into 1 yields [itex]P = \frac{2h\nu}{Ac\Delta t}[/itex]

4) Define Δt as the time it takes for the photons to undergo one round-trip in the box. So, [itex]\Delta t = \frac{2L}{c}[/itex]

5) Plugging 4 into 3 yields [itex]P = \frac{h\nu}{V}[/itex]

6) This can be rearranged to yield [itex]PV=h\nu[/itex]

7) For multiple photons, [itex]PV = Nh\nu_{\text{avg}}[/itex] (since the photon gas is uniform in frequency, [itex]\nu_{\text{avg}} = \nu[/itex])

I believe it's supposed to be [itex]PV=\frac{1}{3}Nhν[/itex], but I can't figure out why! I'm also not sure if that's the right answer, so any clues would be appreciated.

**4. Variables**

P = Pressure, F = Force, A = Area, L = Length, V = Volume (V = A*L), ν = Frequency, t = Time, p = Momentum, c = Speed of light, h = Planck's constant, N = number of photon

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