7d

Question 1

what does <v> mean</v>

Answer 1

its the average molecule speed ( in regards to cartesian coordinates )

Question 2

what does <v> equal to in terms of v's</v>

Answer 2

<v> = Vx2 + Vy2 + Vz2
</v>

Question 3

when at atom moves in any direction,, is movement in each axis equal

Answer 3

yesss
the motion in any direction aka x, y , z is equal

Question 4

if motion in any direction is equal,, what does the equation for v’s equal

Answer 4

Vx2 = Vy2 = Vz2 = <v>2 / 3</v>

Question 5

on average,, what proportion of the molecules collide with a wall + what does this do

Answer 5

on average 1/2 of the molecules will collide with the wall.

across an area of ‘A’

Question 6

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

Answer 6

F = 🔺Px / 🔺T

= (2mvx 🔺xA / 🔺t ) n/2

= mVx 🔺x An / (🔺x/Vx)

= mVx^2 nA

Question 7

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

Answer 7

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

Question 8

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

Answer 8

the partticle collides with the ‘A’ line

this causes a pressure on the containers wall

Question 9

the gas particle collides with the A line which puts pressure on the containers wall,, what is this pressure related to,,

Answer 9

the square of the molecular velocity!!!!!

Question 10

the pressure of the containers wall corresponds to what

Answer 10

P = F/A

which is equal to
mVx^2 n

= 1/3 mn<v>^2
= 1/3M N/V <V>^2</V></v>

Question 11

what can we replace Vx with and what does this give us

Answer 11

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>

Question 12

what if we add the boltzman constant to an equation

Answer 12

1/2 m <v>^2 = 3/2 KBT</v>

bc M = mNa
and KB = R/Na

Question 13

what is the average kinetic nergy of a molecule

Answer 13

3/2 KBT

Question 14

what is the total kinetic energy of 1 mol of a gas

Answer 14

3/2 RT

Question 15

whats P(v)

Answer 15

the probability distribution of molecular velocity, v.

Question 16

what is V

Answer 16

velocity vector

Question 17

what are the components of velocity

Answer 17

vx
vy
vz

Question 18

P(v) dvx, day, dvx is what

Answer 18

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

Question 19

what do we mean when we say boltzman

Answer 19

the probabiltiy that a molecule is in a stage of energy, E, is proportional to

exp ( -E / KBT)

Question 20

what is P(E)

Answer 20

the number of different states in which the molecule has energy

its called the density of states

Question 21

for a gas at thermal equilirbium, the probability of a molecule having translational kinetic energy =

Answer 21

Ekin = 1/2 mv^2

Question 22

v^2 =

Answer 22

Vx^2 + vy^2 + Vz^2

this is proportional to exp(-Ekin / KBT )

Question 23

the probability ,, P(V) (aka the probability distribution) can be written assssss

Answer 23

1/z exp(-mv^2 / 2KBT)

Question 24

what is Z

Answer 24

Z is the normalisation factor

Question 25

whats does Z equal to mathematically

Answer 25

exp ( -mv^2 / 2KBT)

Question 26

the integrat of probability distribution from - infinity to infinity is equal to what

Answer 26

1

Question 27

what can the normalisation factor be calculated from

Answer 27

integral of infinity to - infinity

exp( -mv^2 / 2KBT)

Question 28

1/Z =

Answer 28

(m / 2pi KBT) ^3/2

Question 29

the maxwell distribution,,, of the probability distribution is whattttt

Answer 29

P(V) = (m/2 pi KBT)^3/2 exp(-mv^2 / 2KBT)

Question 30

from the velocity (vector) distribution what can we do

Answer 30

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.

Question 31

what is the probability distribution of molecular speeds

Answer 31

the probability of a molecules speed to be in its normal speed + the difference in its speed

Question 32

what can we define f(V) as and what is this

Answer 32

4 pi P ( V) V^2

this is the probability density for molecular speeds

Question 33

what is beta

Answer 33

m / 2KBT

Question 34

what is M equal to

Answer 34

mNa

Question 35

what is R equal to

Answer 35

KB Na

Question 36

how can we calculate the average speed

Answer 36

<v> integral of Vf(v)dv
</v>

Question 37

the average energy of a single molecular can be calculated as what

Answer 37

< 1/2 mv^2 > = m4 pi / 2Z

= 3/2 KBT

Question 38

the average speed is directly proportinal toooo

Answer 38

the square root of the absolute temp

Question 39

the average speed of a molecule is inversely proportional to what

Answer 39

inverself proportional to itss molar mass.

aka heavier the mass,, smaller the speed

Question 40

the average kinetic energy can be directly linked to what

Answer 40

the absolute temp

Question 41

the average kinetic energy is independent of what

Answer 41

its independent of its mass.

the kinetic energy depends on temp but not the masssss

Question 42

when u plot the probability distribution of molecular velocity against speed!! how does temp affect the plot

Answer 42

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.