Chapter 13 Flashcards
Archimedes said that…
Any object in a fluid that displaces a volume of the fluid that weighs more than the object does, will float upwards in the gravitational field of the earth.
What was this principle used for?
This principle was used by the montgolfier brothers to take flight into the atmosphere using a gas balloon.
What is a gas?
A gas is the simplest form of ordinary matter
Robert boyle was interested in the compression of gases and…
Boyle showed that decreasing the volume of a fixed quantity of air to one half doubles in pressure p.
Increasing pressure
-If you pump more air into a fixed volume, as a constant temp, the pressure is proportional to the ass of the air inside.
Twice amount of air = twice the amount of pressure.
What is Boyles law?
pV = constant
Provided the temp + the amount of gas is constant
What is the relationship between pressure and density?
Pressure ∝ density (at a constant temp)
Bernoulli’s ideas:
- Gases behave in the same way because it is made up of very small rapidly moving molecules
- More often + harder they hit a surface = greater pressure.
Volume and pressure
- The more crowded the molecules, the greater the number of impacts every second with a surface
- Halving the volume occupied by the gas doubles the crowding of the molecules + doubles the pressure.
Equation for pressure and volume
pV = constant x number of molecules
Equation for pressure
p = constant x number of molecules/ volume
Relationship between pressure and volume and mass
p ∝ m/v
As the pressure increases…
So does the temperature
Directly proportional
p ∝ T
As the volume increases…
So does the temperature
Directly proportional
V ∝ T
Pressure and volume are proportional to…
The absolute temperature
What happens when you heat a gas?
- Heated air expands and becomes less dense
- Volume of gas expands with temperature
- Heating the gas increases the pressure in a fixed volume
Charles’ law:
Volume increases linearly with temperature, with a constant pressure
At constant pressure, the volume V of a gas is directly proportional to its absolute temp T
-V/T = constant
The pressure law:
Pressure increase linearly with temperature, with a constant volume
At constant volume, the pressure p of a gas is directly proportional to its absolute temp T
-p/T = constant
Ideal gas law
pV ∝ NT
pV ∝NkT
where k= constant of proportionality
Ideal gas equation
pV = nRT
Where R= universal molecular gas constant
Absolute zero scale
- Absolute zero is given a value of zero kelvin 0K
- At 0K all particles have the minimum possible kinetic energy
- A change of 1K is a change of 1C
How do you calculate/ change from degrees Celsius to Kelvin…
K = C + 273
So if something is given to you in Kelvin and you want to calculate back to degrees, you do C = K - 273
When is kelvin used?
-In all equations in thermal physics
Boyles law
At a constant temperature the pressure p and volume of a gas are inversely proportional
-A theoretical gas that obeys Boyle’s law at all temps is called an ideal gas.
pV = constant
Boltzmann’s constant
-One mole of any gas contains the same no of particles; this number = avogadro’s constant symbol Na (6.02 x 10^23 particles per mole)
-Boltzmann’s constant, k, is equivalent to R/Na
k= gas constant for one particle of gas
R= gas constant for one mole of gas
The equation of state of an ideal gas
pV = NkT
How to work out the number of particle in a mass of gas
N = nNa
where n= number of moles
Na = avogadros constant
Kinetic theory
-The kinetic theory explains the gas laws using the equations for kinetic energy
A particle in a box
-Imagine a particle moves horizontally and hits the wall of the box, this exerts a force on the wall (mv = p) so the particle will head back in the opposite direction.
Particle velocity is proportional to the pressure
-The faster the particle, the larger it momentum, so the larger the force on the wall. The particle will also take less time to travel across the box and back again and so it will hit the walls more frequently. As pressure= force/ are, the pressure will be greater.
The number of particles, N, is proportional to the pressure
-Instead of one particle, the number of particles has increased, each particle exerts a force on the wall and so the total force is proportional to the number of particles. As pressure = force/ area, the pressure is also proportional.
The volume of the box is inversely proportional to the pressure
-The volume of the box decreases and the particles have less distance to travel before they hit a wall, so the frequency of collision increases, which increases the total force on the wall. The area is now smaller so there is a greater pressure.
Particles travel in random directions at different velocities
-You can estimate that a third of all the particles are travelling in one dimension (x, y, z) at any time.
Equation for the pressure
pV = 1/3Nmv̅^2
or p= 1/3Nmv̅^2/ V
Units for v̅^2
m^2s^-2
Simplifying assumptions used in the Kinetic Theory:
- The gas contains a larger number of particles
- A gas consists of molecules of negligible size.
- The molecules collide elastically with each other and the container, on average gaining or losing no energy.
- The molecules are in continual random motion
- There are negligible forces of attraction between the molecules.
- The duration of an impact is much less than the time between impacts.
Gases that obey these assumptions are called…
-Ideal gases, real gases behave like ideal gases as long as the pressure isn’t too big or the temperature too high
Each particle goes on a ‘random walk’
- You cannot record the motion of all the particles in a ga. So instead you can model the movement of the particles by a random walk.
- This assumes each particle starts in one place, moves N steps and ends up somewhere different
- The distance moved on average in those N steps is proportional to √N
The average kinetic energy of a particle is equal to…
3/2kT where k is the Boltzmann constant and T is the temperature in kelvin.
The kinetic model explains the gas laws summarised by the relationship…
pV =NkT
The total internal energy U of an ideal monatomic gas is given by…
U= 3/2NkT
How to calculate the average of v̅^2 (root mean square speed)
r.m.s speed = √v̅^2
Three main sources of evidence for the kinetic model of a gas:
- Expansion into a vacuum
- Diffusion
- Brownian motion
Real gases deviate from…
The predictions of the simple kinetic model
Internal energy
The internal energy U of a number N of molecules of an ideal monatomic gas is
U = 3/2 NkT
where T is the absolute temperature of the gas and k is the Boltzmann constant.
If the temperature of an ideal monatomic gas increases by ∆T…
No change of volume so that no work is done, the internal energy changes by:
∆U = 3/2 Nk∆T
Internal energy definition
Internal energy is the scientific term that replaces what in everyday speech is called the ‘heat’ in a body. The term ‘heat’ is reserved to mean the thermal flow of energy under a temperature difference.
Kinetic energy equation of a molecule…
1/2 mv̅^2 = 3/2kT
per molecule = 3/2kT
Many molecules = 3/2NkT
Expansion in a vacuum and diffusion
-In a vacuum tube, bromine instantly fills the whole tube, but in a tube with air molecules the bromine diffuses. Diffusion is evidence that molecules move. Rapid diffusion into a vacuum is evidence of high molecular speeds. (No collisions)
Brownian motion
-Observation of individual smoke particles using a microscope gives nearly direct evidence. A beam of light directed a a cell containing the smoke, some light is reflected by the particles into the microscope. The particles move in erratic, unpredictable ways, continually changing direction at random. The cause of this motion is continued impacts with the smoke particles and air molecules.
Thermodynamics
If body A and body B are both in thermal equilibrium with body C, then body A and body B must be in equilibrium with each other.
How does thermal equilibrium work if several particles are at different temperatures?
Thermal energy flows through the particles until they all reach thermal equilibrium and the net flow of energy stop when they are at the same temp.
Thermal energy is always transferred from regions of…
Higher temperature to regions of lower temperature.
Thermal capacity
-How much energy it takes to heat something.
The specific thermal capacity (c)
-The amount of energy required to raise the temperature of 1kg of the substance by 1K (or 1 C).
Energy change equation
Energy change = mass x specific thermal capacity x change in temperature.
Symbol equation of energy change
∆E = mc∆θ
where m = mass
c = specific thermal capacity
∆θ = change in temp
The speed distribution of gas particles depends on temperature…
-Particles in a gas travel as different speeds, some particles will be moving faster than others. The shape of the speed distribution depends on the temp of the gas.
As the temperature increases…
- The average particle speed increases
- The maximum particle speed increases
- The distribution curve becomes more spread out
Energy change happens between particles
- Particles are constantly colliding, some will be direct causing them to bounce in opposite directions and some will be pushes from behind.
- As a result energy is transferred between particles, between the collisions particles travel at a constant speed., So the average speed of the particles will stay the same provided the temp of the gas is constant.
Internal energy
The amount of energy contained within a system is the internal energy.
-Internal energy is the sum of the kinetic and potential energy of the particles within a system.
The average kinetic energy is proportional to absolute temperature
1/2mv̅^2 = 3/2nRT/ N
So the internal energy must also be dependant on temperature.
Relationship between absolute temp and kinetic energy
A rise in the absolute temperature will cause an increase in the kinetic energy of each particle, meaning a rise in internal energy.
Energy inside matter =
energy of random thermal motion of particles
Work done =
Force x distance
You can transfer the energy to molecules in two ways
- By hitting the molecules yourself (e.g in a piston)
- Let other molecules hit them (thermal transfer = mc∆θ
Equation for change in internal energy ∆U
∆U = W + Q
Where w = work done
q = thermal transfer
Spontaneous flow of energy from hot to cold =
thermal transfer of energy
How can you test Boyle’s law using compression of a gas?
-Heating up a gas by compressing it is a problem when testing Boyle’s law as temperature needs to be kept constant. When you compress the gas you increase the rate of collisions so you have to give time for the energy to pass to the environment to reduce the heat.
Heating up by thermal transfer:
On average fast moving molecules pass energy onto slow moving ones, until they have the same average energy.
Same average energy =
In thermal equilibrium
First law of thermodynamics
∆U = W + Q
-> It expresses the conservation of energy
First law of thermodynamics expressed as words
change in internal energy = work done x energy transferred thermally.
Energy transferred =
mass x specific thermal capacity x temp rise ∆
∆E = mc∆θ
units of energy transferred
Jkg^-1 K^-1
Mass =
Moles x molecular mass
You may need to change the moles to particles =
A mole = 6 x10^23 particles
Boltzmann constant =
k = 1.4 x 10^-23 JK^-1
Particles in matter at temp T…
Particles in matter at temp T each have energy of the order kT.
Waters specific thermal capacity
-Water has a surprisingly high specific thermal capacity, with important practical and environmental consequences.
Describe how the motion of gas molecules can be used to explain the pressure exerted by a gas on the walls of its container.
Molecules are in constant random motion. When the molecules collide (with the walls) the walls exert a force on the molecules causing a change in their momentum. The molecules exert an (equal and opposite) force (on the walls)creating pressure (as pressure = force/area)
Explain why the molecule does a random walk.
The molecule collides with other molecules and this results in a random/unpredictable change of velocity/ direction
