Derive Radiation Pressure in terms of N, V, hf

• duran9987
In summary, to compute the radiation pressure exerted by a gas of photons with energy hf and perfectly reflecting walls, use the equation P = (1/3)(N/V)(hf/c)^2, where N is the number of photons, V is the volume, hf is the product of energy and frequency, and c is the speed of light. This can also be expressed as P = (1/3)(N/V)(λf)^2, using the equation c = λf.
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.

Use c=λf from the relevant equations?

Related to Derive Radiation Pressure in terms of N, V, hf

Radiation pressure is the force exerted by electromagnetic radiation on a surface, due to the transfer of momentum from the radiation to the surface.

2. How is radiation pressure measured?

Radiation pressure is typically measured in units of force per unit area, such as Newtons per square meter (N/m^2) or Pascals (Pa).

3. What is the equation for calculating radiation pressure?

The equation for radiation pressure is P = (2I/c), where P is the pressure, I is the intensity of the radiation, and c is the speed of light.

4. How can we derive radiation pressure in terms of N, V, and hf?

Using the equation P = (2I/c), we can substitute I with the formula for intensity, which is N x V x hf. This results in the equation P = (2Nhf/cV), where N is the number of photons, V is the volume, h is Planck's constant, and f is the frequency of the radiation.

5. What are some real-world applications of radiation pressure?

Radiation pressure has many practical applications, including solar sails for spacecraft propulsion, optical tweezers for manipulating microscopic particles, and pressure measurement in high-intensity laser experiments.

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