Module 5 Kinetic Theory Flashcards
Describe the experiment which led to the discovery of Brownian motion
Smoke particles which are large enough to be seen under a microscope is added to a small cell containing air
Light from the source is reflected allowing smoke particles to be seen through a microscope
Behaviour of each smoke particle can be observed
Behaviour of air particles (too small to be observed) is deduced from observations of smoke particles
What can be observed in the Brownian motion experiment?
Smoke particles are observed to move in random directions and continuously, constantly changing direction and speed
Explain the observations in the Brownian experiment
Smoke particles are bombarded from all sides by air molecules
Air molecules most move randomly and continuously
Air molecules are too small to be seen
State the four assumptions of kinetic theory
Large number of molecules in continues random motion at high speed
All collisions between molecules are perfectly elastic and the time in collisions is negligible to time between collisions
Negligible forces between molecules except during collision
Volume of molecules is negligible compared to volume of container
Explain how change in momentum is calculated for molecules colliding with an object
Particle with mass collides with wall and rebounds with same speed v (elastic collision)
Therefore final momentum equal but opposite to initial momentum
Change in momentum = mv-(-mv) = 2mv
Explain air pressure using kinetic theory
Molecules collide with wall and rebounds so momentum changes direction
Newtons second law states that the rate of change of momentum is equal to a force, thus a force is exerted on the molecules
Newtons third law states that an equal and opposite force must be exerted on the wall
Pressure = sum of forces on wall from many molecules/area
Explain Boyle’s law using kinetic theory
(that is pressure inversely proportional to volume)
When VOLUME IS REDUCED at constant temperature molecules have the same KE, momentum and speed.
More frequent collisions with surface, same momentum
PRESSURE WILL RISE
Explain the pressure law using kinetic theory
Temperature is increased thus molecules gain KE (E=3/2kT), momentum and speed
Each collision produces more force and particles collide with walls more frequently
Pressure increases
Explain and derive an equation for pressure using number of molecules (P=Nmv^2/V)
A particle moves at speed v with it’s change of momentum in a rebound being = 2mv
in one second particle moves a distance of v
Distance between 2 collisions is 2L
In one second the number of collisions = v/2L
total change in momentum = 2mv * v/2L
Simplified to mv^2/L in one second (therefore force is the same as the equation)
Multiplied by number of particles
For a given volume (V=L^3 (think about a cube)
P=Nmv^2/V
Alternative equation for pressure using number of particles and volume
P=Nmv^2/V
P pressure
N number of particles
m mass of each particle
v speed
V volume
What is c^2 bar also known as?
mean square speed
What is the m in the pressure equation using mean square speed?
P=Nmv^2/V
mass of a single atom
Variation of an equation using pressure using mean square speed involving density
P=1/3 x density x c^2
What is the notation for root mean square speed?
crms
What can be said about the difference between root mean square speed and the mean speed?
similar but mean speed is slightly lower than root mean square speed
What does the Maxwell Boltzmann distribution have on the axis in physics?
number of particles (on y axis) vs speed of particle (on x axis)
Describe the order of mean speed, root mean square speed, and mode speed on a Maxwell Boltzmann distribution curve
(smallest) mode, mean, root mean square speed (biggest)
Explain how the Boltzmann constant was discovered
PV=nRT version with number of moles n
is modified to include number of molecules
PV=(N/Na)RT
R/Na is a constant which is the Boltzmann constant
PV= NkT
Explain how the equation for kinetic energy using T is derived using given equations
PV=1/3Nmc^2
PV=NkT
Means NkT=1/3Nmc^2
N cancels out
Cancel out 1/3 to give mc^2=3kT
Divide both sides by 2 to get 1/2mc^2=3/2kT
First half is average KE of one particle
What two equations must be used to derive E=3/2kT?
PV=1/3Nmc^2
and
PV=NkT
Explain how root mean square speed can be found for mixtures of gases using temperature
1/2mc^2=3/2kT
Can find individual speeds of gases of different masses
Explain the relationship between U and T for gases
For ideal gases there is no PE
U is total KE of all particles
3/2kT=E energy of one particle
U=3/2kT*N
U and absolute T are directly proportional
Explain how changes in U can be calculated using changes in T without knowing number of molecules involved?
KE = 3/2kT (multiply by N to get U)
KE/T = constant
KE1/T1=KE2/T2 with T in Kelvin
Explain how thermal equilibrium is reached
When two gases mix of different temperatures
Gas particles with higher KE will transfer some KE to particles with lower KE on average
Until the average is reached
All particles have the same average KE and temperature
What is thermal equilibrium and what does it mean in terms of calculations?
when two substances have the same temperature
and therefore the same mean KE (for gases)
If two different substances are at the same temperature, what can be said about their motion?
same KE
different root mean square speeds if mass of molecules is different
high mass, lower speed
How can U for a gas be calculated?
average KE of one particle*number of particles N
or
3/2kT times N
How do can you ensure accuracy in results when using a pressure gauge and a conical flask full of gas in a thermostatically controlled water bath to measure the relationship between pressure and volume?
Clamp flask below surface of water
Thin rubber tubing so volume of gas in tubing is negligible
Heat water to 100ºC and then cool when taking measurements
To ensure air is in thermal equilibrium with water
