7d Flashcards
(42 cards)
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
