THERMAL PHYSICS Flashcards
1st law of thermodynamics
Change in internal energy of object = total energy transfer due to work done and heating
Fun fact about graduations of thermometer
Interval distance isn’t the same at the middle of the scale vs ends (measure w travelling microscope) - expansion of liquid isn’t directly proportional to temperature
When does energy transfer occur?
When one object exerts a force on another object, causing it to move (does work), or when one object is hotter than another, so energy is transferred via convection, conduction or radiation
Conditions for constant internal energy
No work done/energy transfer by heating or energy transfer by heating and work done “balance each other out”
What is internal energy?
The sum of the random distribution of the kinetic and potential energies of its molecules
Boyle’s law
pV = constant for constant temperature + n
Charles’ Law
V/T = constant for constant pressure + n
isobaric meaning
At a constant pressure
Pressure and temperature relationship
P/T is constant
Work done in terms of p &V
E=pΔV
Avocado constant definition
Number of atoms in 12g of carbon12
Atomic mass unit defintion
1/12 the mass of a carbon12 isotope
1 Mole definiton
Molar mass definition
Quantity of a substance (identical particles) that contains Nₐ particles
= (Mass/μ)
Molar mass - Mass in 1 mole = Molxμ
mew is atomic mass
Ideal gas eq
pV = nRT
graph of pV against T is straight line through absolute zero
Manipulating ideal gas law (in terms of density and number of molecules)
n=pV/RT Mₛ=Mn (mass=molarmassxn)
Mₛ = MpV/RT → ρ=Mp/RT for molar mass M
or nM/V
n=N/Nₐ where N is number of molecules
pV = NkT where k = R/Nₐ (boltzmann constant)
Assumptions made in kinetic theory
- Molecules are point molecules - volume of
each molecule negligable wrt volume of gas - Molecules don’t attract each other (would
reduce force on impact with container) - Move around in continual random motion
- Collisions with other molecules and
container are elastic - Each collision with the container is of
much shorter duration than the time
during impacts
Getting p = NM/3V
Pₓ = (NMvₓ^2)/V and etc for Pᵧ and P₂
so 3P = NM/V (Pₓ^2+Pᵧ ^2+ P₂ ^2)
P = NM/3V (c^2) where c = rms
also u^2 = 1/N(u1^2+u2^2…un^2)
as c²=x²+y²+z²
crms = c²+c²+c²…cn²/n
= x²+y²+z² … xn²+yn²+zn²/n
= xrms²+yrms²+zrms²
What happens to arrangement of atoms during state change specifically
Energy transferred reduced number of nearest atomic neighbours
(crystalline to amorphous from solid to liquid)
atoms move to centre of vibration
also avoid using velocity instead of speed when talking abt motion
Deductions from experiment where Brownian motion is demonstrated using smoke particles in air
The motion is caused by collisions between air molecules
and smoke particles
Ideal gas law + kinetic theory interpretations of absolute zero
Ideal gas - where pressure/volume =/(extrapolates to) 0
Kinetic- random motion stops or Ek of particles = 0
Compare mean Ek of two types of particles enclosed in a volume at the same temp
System is at equilibrium so same mean Ek
Explain using kinetic theory model why a gas exerts a force on a piston
Particles collide with piston and change momentum
Force = rate of change of momentum
Pressure = force/area
Using the kinetic theory model, two changes that can be made independently to
reduce the pressure exerted by a gas
change
the volume could be increased
explanation
which increases the time between collisions OR results in less frequent collisions
(with the piston/wall so reducing the rate of change of momentum)
OR
which increases the area of the piston/wall (and so reduces the pressure)
change
the temperature could be reduced
explanation
which reduces the momentum (change at the wall)
Which of the following is not an assumption of the kinetic model of ideal gases?
A. All particles in the gas have the same mass.
B. All particles in the gas have the same speed.
C. The duration of collisions between particles is very short.
D. Collisions with the walls of the container are elastic.
C - The particles have a distribution of speeds with a mean (temp)
Under what conditions of density and pressure is a real gas best described by the equation of state
for an ideal gas?
A. Low density and low pressure
B. Low density and high pressure
C. High density and low pressure
D. High density and high pressure
A - Large distance between particles
Derivation of kinetic theory steps
Find the change in momentum as a single molecule hits a wall perpendicularly. …
Calculate the number of collisions per second by the molecule on a wall. …
Find the change in momentum per second. …
Calculate the total pressure from N molecules. …
Consider the effect of the molecule moving in 3D space
Mean velocity of a gas
Zero, as there are equal distributions in all directions (pos and neg)
arguable
Mean speed
Sum of speeds divided by number of molecules
Graph of number of molecules with speed v against v
Kinda bell distribution - If temperature of gas increases, curve becomes broader and flatter - greater number of particles moving at greater speeds. Also slightly shifted to right
Internal energy of an ideal gas
Only due to kinetic energy of molecules
= total Ek/N
= m/2 (c1²+c2²…cn²)/N
mcrms²/2
Higher temperature higher mean Ek
Average translational Ek of a gas molecule
3/2 KT = 1/2mcrms²
Monatomic atoms have translational Ek, however diatomic have rotational aswel
Monos basically points
energy of n moles using 3/2KT
3/2nKT aka 3/2nRT from equating pv in ideal gas eq and kinetic theory
Limitations of kinetic theory
When the temperature is low and the pressure is high, the molecules come closer to each other, and the volume of the gas is compressed. In this scenario, one cannot ignore the forces of attraction between them and the volume of the gas.
Why can’t kinetic theory be applied to liquids and solids?
The kinetic theory modelling assumes that the molecules are very small relative to the distance between molecules. This is certainly not true of liquids and solids
Gas laws vs kinetic theory
Gas laws are empirical however kinetic theory model arises from theory
Brownian motion proving existence of atoms
Pollen grains in water move w zigzag motion
- Movement of particles suspended in a fluid - brownian
- Says that random motion is due to collisions with fast, randomly moving particles in fluid.
Seen when large heavy particles (smoke) are moved with Brownian motion by smaller lighter particles (air) travelling at high speeds. Evidence that air is made up of tiny atoms/molecules moving quickly
Brownian motion
Brownian motion:
Can be observed under a microscope
Provides evidence for the existence of molecules in a gas or liquids
The particles are said to be in random motion, this means that they have:
A range of speeds
No preferred direction of movement
The observable particles in Brownian motion are significantly bigger than the molecules that cause the motion
In most cases, these were observed as smoke particles in air
The air particles cause the observable motion of the smoke particles that we see
This means that the air particles were small and light and the smoke particles were large and heavy
The collisions cause larger particles to change their speed and directions randomly
This effect provides important evidence concerning the behaviour of molecules in a gas, especially the concept of pressure
The small molecules are able to affect the larger particles in this way because:
They are travelling at a speed much higher than the larger particles
They have a lot of momentum, which they transfer to the larger particles when they collide
When internal energy may not be due to thermal energy
A magnetised iron bar has a greater internal energy than an unmagnetised one due to the magnetic interaction between the atoms in the bar
What is a molecule
Smallest particle of a pure substance that is characteristic of the substance
Solids
Atoms/molecules held together by forces due to electric charge of protons/electrons in atoms. Molecules vibrate randomly about fixed positions, higher temperature greater vibration. If enough energy provided molecules vibrate so much they break free from each other (crystalline to amorphous), raising potential energy
Liquids
Molecules move randomly in contact with each other - higher temperature faster movement
Vapours
Molecules move randomly at greater distances than those in a liquid
Absolute zero
No object can have a temperature below absolute 0. An object at absolute 0 has minimum internal energy
Improving the thermal contact between thermometer and metal
Use a small amount of water/oil
pg41 year 2
Before you measure the temperature of a liquid in an experiment
Give it a stir
Sublimation
When an object vaporises immediately when heated
Pressure of a gas
Force per unit area exerted normally on a surface
Depends on temperature, volume and mass of gas in container
Why pv is work done
When work is done to change the volume of the gas, energy must be transferred by heating to keep pressure constant.
(for constant pressure)
Explaining Boyle’s law experimentally
Pressure of a gas at constant T is increased by reducing the volume as the gas molecules travel less distance between impacts with the walls due to reduced volume. More impacts per second - greater pressure
Explaining pressure law experimentally
Pressure of a gas at constant volume is increased by raising its temperature. Average speed of molecules increases with temperature. Therefore greater change of momentum on impact as well as greater number of impacts per second - greater pressure
Molecular speeds
In an ideal gas have a continuous spread of speeds. Speed of an individual molecule changes when it collides with another gas molecule, but distribution doesn’t change as long as T is constant
