Kinetics, Thermal Conductivity, Diffusion, Mean Free Path Flashcards
Kinetics & Transport Theory
Transport Theory - How heat, mass, and momentum move throughout a system.
Kinetics - study of motion and interactions of particles in molecular level
Heat Conduction
Heat transfer by direct contact at the molecular level (molecular collisions) (solid, liquid, or gas)
Fast molecule hits a slow molecule
ΔQ = AΔTΔt/Δx —> Q/Δt = A dT/dx —> Q/Δt = -kt A dT/dx
Fourier Heat Conduction Law ^
Δx = thickness, Δt time
where kt = thermal conductivity; negative because if T increases from left to right, Q flows from right to left.
Resistance of Material
R = Δx/kt
Conductivity of an Ideal Gas: What limits heat conduction?
How far a molecule can travel before colliding with another molecule.
Mean Free Path
Average distance traveled between collisions.
Collision is defined as when the center of a molecule comes within one molecular diameter of center of another molecule.
Volume of Cylinder = Average Volume Per Molecule
π(2r)^2 l = V/N
l = 1/4 πr^2 V/N
(rough approximation; neglecting motion of other molecules and variation in path length between collisions)
Average Time Between Collisions
Δt = l/vrms
Net Heat Flow
Q = 1/2 (U1 - U2) = -1/2 (U2 - U1) = -1/2 Cv (T2-T1) = -1/2 Cvl dT/dx
How does thermal conductivity relate to the average speed of the molecules?
kt = 1/2 Cvl/AΔt = 1/2 Cv/Al l^2/Δt = 1/2 Cv/V l v
Cv/V = (f/2)Nk/V = f/2 P/T
Proportional Variables
l = V/N
v = (T)^1/2
L^2 = Dt = lvt
D = lv
Viscosity
Resistance of fluid’s flow
Spread of momentum in a fluid at molecular level.
|Fx| / A = n du/dz
where du is flow, z is direction of flow and change in z is length in between two surfaces. (length of fluid)
Diffusion
Flow of Process where particles move from regions of high to low concentration from random molecular motion.
Particle Flux
J = -D dn/dx —> N/AΔt = D(N/V/Δx)
n is particle concentration, D is diffusion coefficient
Relaxation Time
dC/dt = D(d^2C/dx^2)
l^2 =1 L² 2Dt
t = l^2/2D
