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
[def] mole
SI unit for “amount of a substance”: it is the amount containing as many particles as there are ATOMS in 12g of Carbon-12
Moles equation
total mass(in GRAMS) / molar mass
what IS boltzman constant?
k = R/Na
KE per mole
KE per molecule
KE PER MOLE = 3/2 * RT
KE PER MOLECULE = 3/2 * kT
[def] Internal energy of a system, U
Sum of the kinetic and potential energies of the particles of a system
[def] Absolute Zero
temp of a system when it has minimum internal energy
0Kelvin = -273 degC
What does equation
U = (3/2)nRT = (3/2)pV
mean?
Internal energy on an IDEAL MONATOMIC GAS
–>because only KINETIC
[def] Heat, Q
Energy FLOW from a hot object to a cold object
when they are in THERMAL CONTACT
–> heat either going in or out ~(in transit)~ not “contained”
Temperature
Measure of the average KE of particles in a system
Thermal Equilibrium
When no heat flows between systems in contact therefore same temp
[def] Work, W
Work is energy in transit from or to a system
W=pΔV = pressure * increase in volume WHEN AT CONSTANT PRESSURE
–> W= area under PV graph, even at non constant pressure
Work gas equation derivation (x3 steps)
W=Fx
W=PAx
W=PV
ASSUMES PRESSURE IS CONSTANT
[Def] First Law of Thermodynamics
Conservation of energy in the system
Q = ΔU + W
Q = ΔU + W
what is meant by +ve Q?
what is meant by +ve U?
what is meant by +ve W?
Q = ΔU + W
increasing Q = +ve
Increasing U = +ve
work done BY gas = +ve W
work done ON gas = -ve W
Conditions when W is can be ignored in first law of thermodynamics
For a SOLID (or LIQUID)
W is usually negligible
so
Q = ΔU
[def] Specific heat capacity, c
Amount of energy required to raise 1kg of a substance by 1K
UNIT: J kg-1 K-1
