Thermal

• Kelvin is the main temperature scaled used in science, it is the same as Celsius +273
• Absolute zero is at 0 kelvin (-273 Celsius) and is the lowest possible temperature as the molecules have 0 kinetic energy
• The internal energy of a body is the sum of all the randomly distributed kinetic and potential energies of all its particles
• In a gas, the speed of the particles are not consistent and follow a distribution. The higher the temperature, the wider the distribution curve.
• A closed system is one that doesn't allow any transfer of matter in or out. The internal energy remains constant.
• The specific heat capacity of a substance is the amount of energy needed to raise the temperature of 1 kg by 1 kelvin.

  Energy change = mass * specific heat capacity * temperature change

  Q = m c Δθ
• When a material changes state, the kinetic energy and temperature stay constant but the internal energy changes due to the potential energy changing
• What are the 2 types of latent heat?

  Fusion (solid - liquid)

  Vaporisation (liquid - gas)
• Boyles law states at a constant temperature, the pressure is inversely proportional to the volume of an ideal gas

  p V = constant
• Charles law states that at a constant pressure, the volume is directly proportional to its absolute temperature.

  V / T = constant
• The pressure law states that at a constant volume, the pressure of an ideal gas is directly proportional to its temperature

  p / T = constant
• At absolute zero, the pressure is zero, the temperature is zero and the volume is theoretically zero as well
• Relative molecular mass is the sum of all the relative atomic masses (mass found from the periodic table)
• Avogadros constant is the number of particles in one mole of a substance
• The molar mass of a substance is the mass of 1 mole which is just the relative atomic mass in grams
• From the 3 gas laws, you can derive an ideal gas equation which is pressure * volume / temperature = constant

  p V / T = constant
• Using pV/T at room temperature with 1 mole of gas at atmospheric pressure, you get the molar gas constant R

  From this constant you get:

  p V = n R T

  p = pressure, v = volume, n = number of moles, R = molar gas constant, t = temperature
• The boltzmann constant k is equal to R/Na

  From this we have another ideal gas equation for molecules instead of moles:

  p V = N k T

  p = pressure, V = volume, N = number of molecules, k = boltzmann constant, T = temperature
• When changing the volume of a gas, work is done to do this

  work done = pressure * change in volume (area under a pressure volume gas)
• To derive the pressure of an ideal gas you need to start with a cubic box with length l containing N molecules with mass m
• Step 1 in deriving pressure of an ideal gas

  Say molecule Q moves directly towards one of the walls with a velocity of u, When it strikes the wall it will rebound in the opposite direction and assuming the collision is perfectly elastic, the change in momentum is

  -mu - mu = -2mu
• Step 2 in deriving pressure of an ideal gas

  After rebounding the wall, assuming there are no other collisions with other molecules, the time between collisions of the particle Q and the original wall is 2l/u so the number of collisions is u/2l

  The rate of change of momentum is therfore -2mu * u/2l
• Step 3 in deriving pressure of an ideal gas

  From newtons second law we get force=rate of change of momentum which is -mu^2/l

  From newtons third law, the molecule exerts an equal and opposite force on the wall so is mu^2/l
• Step 4 in deriving pressure of an ideal gas

  There are many molecules in the gas so we can find an average squared velocity summing the square of them all (we do this to avoid the negative signs) and this gives us the mean square speed.

  Since the total force is m(u1+u2+u3)/l, using this mean square speed we get:

  F=NmU^2/l

  Where U^2 is the mean squared speed of all the particles

  N=number of particles

  m=mass of one particle

  l=length of box
• Step 5 in deriving pressure of an ideal gas

  pressure=force/area

  in our little box this gives us:

  (NmU^2/l) / l^2

  NmU^2/l^3

  NmU^2/V

  N=number of molecules

  m=mass of one molecule

  U^2=mean square speed

  V=volume
• Step 6 in deriving pressure of an ideal gas

  Since molecules can move in 3 dimensions, the mean square speed = mean square speed of all 3 dimensions

  Since molecules move randomly, all 3 of these dimensions are equal so

  C^2=3u^2

  putting this into the equation give us the final equation of:

  p V =1/3 N m C^2

  C^2=mean square speed
• The root mean square speed is the mean square speed square rooted
• From the kinetic model, we can explain Charles law and the pressure law:

  As the temperature increases, the average speed increasing increasing the change of the momentum therefore increasing the force and volume of container

  However if the volume is fixed, this will instead increase the pressure as there will be more collisions between the molecules are the walls of the container
• Assumptions in the kinetic theory:

  All molecules of the gas are identical

  The gas contains a large number of molecules

  The molecules have negligible volume

  The molecules move randomly

  Newtonian mechanics apply

  All collisions are perfectly elastic

  The time the force acts is minimal

  The molecules move in a straight line between collisions
• Using the kinetic theory you get that average kinetic energy = 3/2 nRT/N which using the boltzmann constant turns into 3/2 kT which is 3/2 RT/Na
• Boltzmann constant k = R/Na which gives us:

  Nk=nR

  N=number of molecules

  n=number of moles

  R=molar constant
• Total kinetic energy of molecules = average kinetic energy * number of molecules
• Empirical laws are based on observation and evidence.

  They can predict what will happen but done explain why like the gas laws
• A theory is based on assumptions and derivations and will predict and explain why a change will occur like the kinetic model theory
• Theorys have to be validated before its widely accepted to be true
• Brownian motion is the random movement of particles in a liquid or gas.