5.1 Thermal Physics

• Triple point of a substance is a certain pressure and temperature where the three phases of matter can exist in thermal equilibrium
• Thermal equilibrium - where there is no net transfer of thermal energy
• Temperature is a measure of how hot something is - it is not related to the internal energy of a substance
• The 0th law of thermodynamics

  If two objects are in thermal equilibrium with a third, then all three objects are in thermal equilibrium
• The two fixed points on the celcius scale are the freezing and boiling points of pure water

  It is imperfect as it fails to recognise that water can boil at a temperature as low as 70C
• The absolute temperature scale uses the triple point of water and absolute zero as fixed points
• Absolute zero is the lowest possible temperature of a substance wherein particles have no kinetic energy and the substance has minimal internal energy
• A temperature difference in 1K is the same as a temperature difference of 1C as they have equal increments but where T is used in equations, the absolute temperature must be used
• Temperature in Kelvin is $\theta+$273
• The kinetic model describes that all substances are made up of atoms or molecules which are arranged differently depending on the phase of the substance
• A solid has particles arranged uniformly and close together with strong electrostatic forces holding them together but still allowing them to vibrate so they have kinetic energy
• Liquids have particles close together but have more kinetic energy than in solids and can flow past each other and change position
• In gases, particles have a lot of kinetic energy and there is negligible electrostatic attraction between particles> Particles are free to move past each other and often occupy a large volume
• Brownian motion - particles move in random directions at different speeds and have an average velocity of 0
• Brownian motion provides evidence for the kinetic model as matter is made up of molecules that vibrate and move
• Brownian motion can be observed through pollen grains in a liquid through a microscope or a smoke cell
• Electrostatic potential energy refers to the energy stored between particles. It is always negative as energy is required to break apart particles
• Internal energy of a substance increases when temperature increases as the total kinetic energy of the particles increases
• Internal energy increases as a substance changes phase - melting and evaporation only. There is no change in kinetic energy of the particles, however internal energy increases due to the increase of electrostatic potential energy required to break the bonds
• Specific heat capacity is the energy required to increase the temperature of 1kg of a substance by 1 degree
• Method of mixtures

  Known masses of two substances at different temperatures are mixed together. Recording their final temperature at thermal equilibrium allows for the specific heat capacity for one substance to be calculated if the other is known
• Specific latent heat is the energy required to change the phase of a substance per unit mass while at a constant temperature
• Specific latent heat of fusion is the heat per unit mass required to change a solid to a liquid
• Specific latent heat of vaporisation is the energy per unit mass to change a liquid to a gas
• Specific latent heat of vaporisation is often much larger than the specific latent heat of fusion as the difference of electrostatic forces between particles in a liquid and gas are greater than the difference between electrostatic forces between particles in a liquid and solid
• When an object condenses or freezes, it loses energy, making it an exothermic reaction
• One mole is the amount of substance that contains as many elementary entities as there are in 12g of C-12
• Avogadro constant - $6.02\ \times10^{23}$

  number of atoms in 12g of C-12
• Gases exert pressure on their containers as particles in the gas move around and collide with the container, exerting a force over an area
• The total change in momentum when a gas elastically collides with the wall of the container is -2mu if the positive direction is towards the wall
• If temperature and mass remain constant, pressure is inversely proportional to its volume
• Boyle's Law

  $pV=$$nRT=$$NkT$

  p - pressure

  V - volume

  n - number of moles

  R - molar gas constant, 8.31

  T - temperature

  N - number of particles

  k - Boltzmann constant, 1.38 x 10^-23