The momentum transfer to the container wall from particles hitting the area d A with speed v at angle θ θ from the normal, in time interval d t is: [ 2 m v cos ⁡ ⁡ ( θ θ ) ] × × n v cos ⁡ ⁡ ( θ θ ) d A d t × × ( m 2 π π k B T ) 3 / 2 e − − m v 2 2 k B T ( v 2 sin ⁡ ⁡ ( θ θ ) d v d θ θ d ϕ ϕ ) . Integrating this over all appropriate velocities within the constraint v > 0 , 0 < θ θ < π π / 2 , 0 < ϕ ϕ < 2 π π yields the pressure (consistent with Ideal gas law): P = 2 ∫ ∫ 0 π π / 2 cos 2 ⁡ ⁡ θ θ sin ⁡ ⁡ θ θ d θ θ ∫ ∫ 0 π π sin ⁡ ⁡ θ θ d θ θ × × n m v rms 2 = 1 3 n m v rms 2 = 2 3 n ⟨ ⟨ E k i n ⟩ ⟩ = n k B T If this small area A is punched to become a small hole, the effusive flow rate will be: Φ Φ effusion = J collision A = n A k B T 2 π π m .