7d Flashcards
what does <v> mean</v>
its the average molecule speed ( in regards to cartesian coordinates )
what does <v> equal to in terms of v's</v>
<v> = Vx2 + Vy2 + Vz2
</v>
when at atom moves in any direction,, is movement in each axis equal
yesss
the motion in any direction aka x, y , z is equal
if motion in any direction is equal,, what does the equation for v’s equal
Vx2 = Vy2 = Vz2 = <v>2 / 3</v>
on average,, what proportion of the molecules collide with a wall + what does this do
on average 1/2 of the molecules will collide with the wall.
across an area of ‘A’
when ur moving along the x axis and colliding with a wall of area ‘ A ‘,, force on a wall due to momentum change is what
F = 🔺Px / 🔺T
= (2mvx 🔺xA / 🔺t ) n/2
= mVx 🔺x An / (🔺x/Vx)
= mVx^2 nA
okay so we have 2 lines paralel to each other,, with both of them pointing up,, what are the lines labelled as,, and what is the difference between the 2 lines,, and what is the image that completes it
okay so the lines are labelled as A ( the one that that gas particle is colliding with)
the difference between the 2 lines is 🔺x.
the bit that completes the diagram is a particle with arrows pointing at the ‘A’ line and back off into space between the two lines.
arrow towards the line ‘A’ = mVx
arrpw away from the ‘A’ =
–mVx
okay so we have the diagram of the gas particle colliding with the ‘A’ line and being bounced back off,, what does the gas particle do to the containers wall
the partticle collides with the ‘A’ line
this causes a pressure on the containers wall
the gas particle collides with the A line which puts pressure on the containers wall,, what is this pressure related to,,
the square of the molecular velocity!!!!!
the pressure of the containers wall corresponds to what
P = F/A
which is equal to
mVx^2 n
= 1/3 mn<v>^2
= 1/3M N/V <V>^2</V></v>
what can we replace Vx with and what does this give us
1/3<v></v>
bc <v> is the sum of all the v's</v>
and theres 3 v’s : x,y,z
so RT = 1/3 M <v>^2</v>
what if we add the boltzman constant to an equation
1/2 m <v>^2 = 3/2 KBT</v>
bc M = mNa
and KB = R/Na
what is the average kinetic nergy of a molecule
3/2 KBT
what is the total kinetic energy of 1 mol of a gas
3/2 RT
whats P(v)
the probability distribution of molecular velocity, v.
what is V
velocity vector
what are the components of velocity
vx
vy
vz
P(v) dvx, day, dvx is what
the molecule fraction whos velocity vector components are in the range
of the original vector + the change in the original vector.
aka point vx + dvx
what do we mean when we say boltzman
the probabiltiy that a molecule is in a stage of energy, E, is proportional to
exp ( -E / KBT)
what is P(E)
the number of different states in which the molecule has energy
its called the density of states
for a gas at thermal equilirbium, the probability of a molecule having translational kinetic energy =
Ekin = 1/2 mv^2
v^2 =
Vx^2 + vy^2 + Vz^2
this is proportional to exp(-Ekin / KBT )
the probability ,, P(V) (aka the probability distribution) can be written assssss
1/z exp(-mv^2 / 2KBT)
what is Z
Z is the normalisation factor
whats does Z equal to mathematically
exp ( -mv^2 / 2KBT)
the integrat of probability distribution from - infinity to infinity is equal to what
1
what can the normalisation factor be calculated from
integral of infinity to - infinity
exp( -mv^2 / 2KBT)
1/Z =
(m / 2pi KBT) ^3/2
the maxwell distribution,,, of the probability distribution is whattttt
P(V) = (m/2 pi KBT)^3/2 exp(-mv^2 / 2KBT)
from the velocity (vector) distribution what can we do
we can obtain the probability distribution of molecular speed, which is the probability of molecular speeds to be in the range of the original + the difference.
what is the probability distribution of molecular speeds
the probability of a molecules speed to be in its normal speed + the difference in its speed
what can we define f(V) as and what is this
4 pi P ( V) V^2
this is the probability density for molecular speeds
what is beta
m / 2KBT
what is M equal to
mNa
what is R equal to
KB Na
how can we calculate the average speed
<v> integral of Vf(v)dv
</v>
the average energy of a single molecular can be calculated as what
< 1/2 mv^2 > = m4 pi / 2Z
= 3/2 KBT
the average speed is directly proportinal toooo
the square root of the absolute temp
the average speed of a molecule is inversely proportional to what
inverself proportional to itss molar mass.
aka heavier the mass,, smaller the speed
the average kinetic energy can be directly linked to what
the absolute temp
the average kinetic energy is independent of what
its independent of its mass.
the kinetic energy depends on temp but not the masssss
when u plot the probability distribution of molecular velocity against speed!! how does temp affect the plot
a lower temp = a larger probabiltiy distribution + smaller speed
a higher temp = smaller probability distribution of molecular velocity,, and a larger range of speed,,, but it also reaches higher speeds.
