Kinetic Theory, Thermal Physics Flashcards
[def] Ideal Gas
A gas which strictly obeys the equation of state pV=nRT (and define terms)
with exeption of very high densities, a real gas approximates well to an ideal gas
pV=nRT define terms
p= pressure V= volume n= number of MOLES R= Molar gas constant T= temp IN KELVIN
pV = NkT define terms
p= pressure V=volume N= number of MOLECULES k= Boltzman constant T= temp in KELVIN
Ideal gas assumptions (x5) –> inc way to remember!
- no [I]ntermolecular forces ——————[i]
- [V]olume of each particle is negligible -[Value]
- all collisions are [E]lastic ——————-[Energy]
- [R]andom motion ——————————[Real]
- negligible effect of [G]ravity ————-[Good]
PV graph
describe
conditions
ALWAYS CURVED DOWN
Constant mass, constant temp
higher temps = on top
P- 1/V graph
Straight lines
higher tempts = steeper grad
Kinetic Theory
random distribution of energy amongst molecules
Why gas exerts pressure? (X4)
Molecular movement =more collisions =more Δ momentum (per collision AND per unit time) = greater force (Δmv = Ft) = greater pressure
rms meaning
root mean square
switch (Nm)/V to density
density ρ = mass/ volume * for all molecules N
Use in equations given for pressure
P=1⁄3(Nm)/V (c squared bar, rms)
P=1⁄3ρ(c squared bar, rms)
P=1⁄3*(Nm)/V *(c squared bar, rms) derivation
first 4 steps
- momentum = m*(Vin x direction)
- Elastic collision with wall Δ momentum after = -2m*(Vin x direction)
- Force per unit time ON PARTICLE Ft= -2m*(Vinx dir)
- Force on Wall F= (2m(Vinx))/t
P=1⁄3*(Nm)/V *(c squared bar, rms) derivation
time between collisions on wall (step 5)
step 6 step 7
- time between collisions on this wall
t= (2l)/(Vinx dir) - combine with step 4
- multiply for N molecules
P=1⁄3*(Nm)/V *(c squared bar, rms) derivation
Consider average Vinx direction (step 8)
Why?
How?
- because molecules moving at different speeds
split velocity into 3 components
c= Vinx + Viny +Vinz
c^2 = Vinx^2 + Viny^2 +Vinz^2
AND Vinx^2 = Viny^2 = Vinz^2 Or else box would drift away!
avg c^2 = 3(Vinx^2)
Vinx^2 = (avg c^2)/3
P=1⁄3*(Nm)/V *(c squared bar, rms) derivation
steps 9, 10, 11
- combine steps 8 and 7
F= (Nm(c^2avg))/3L - P=F/A divide by area
L^3 = volume
P=1⁄3(Nm)/V (c squared bar, rms)
PV= 1⁄3(Nm)(c squared bar, rms)
[def] Avogadro Constant, Na
Number of particles per mole
6.02 x10^23
