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Derive Radiation Pressure in terms of N, V, hf

  1. Jan 25, 2016 #1
    1. The problem statement, all variables and given/known data
    Compute the radiation pressure exerted by a gas of photons (according to kinetic theory). There are N photons, each with energy hf, the momentum is hf/c, and the walls are perfectly reflecting. Express the pressure in terms of N, V, and the product hf.

    2. Relevant equations
    Pressure = (1/3)*(Nk/V) (mv^2) , where v^2 is an average
    Pressure = Force / Area
    Speed of Photons = λf
    Force on Area A = (Number of collisions on the wall in time Δt)(Momentum transferred to the wall per collision)/(Δt)

    3. The attempt at a solution
    The momentum transferred to the wall by the photons is 2(hf/c)
    The number of collisions = ((λf)ΔtA)(1/2)(N/V)
    Force on Area A = (hf/c)(A)(N/V)(λf)
    Multiply both Sides by Area to get pressure = P = (1/3)h(f^2)λ(N/V)(1/c)

    Not sure how to express it in terms of the product hf.



     
  2. jcsd
  3. Jan 25, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Use c=λf from the relevant equations?
     
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