Derive Radiation Pressure in terms of N, V, hf

[duran9987]

Homework Statement

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.

Homework 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)

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.

 

[mfb]

Use c=λf from the relevant equations?