Particle model of matter

• Macroscopic world VS. microscopic world​

• Matter is consisted of small structures: Molecules...Atoms...Quarks, known as Particles.

• Inter-particle forces: "Spring-like" bonds between particles.

  • Bond force: Solid (s) > Liquid (l) > Gas (g) - phases of matter.

 

Absolute temperature​​

• "Absolute temperature is proportional to the average random kinetic of the molecules".

• Absolute temperature = T (in kelvin, K) = Temperature in degrees Celsius (ºC) + 273

  • Absolute zero (0 K): Zero Kinetic energy (theoretically).

  • Triplet point of water (273 K): water can be in any of the 3 phases.

 

Internal energy​

"The internal energy of a substance is the total potential energy (due to inter-molecular bonds between particles) and the total random kinetic energy of all the molecules in the substance." It can change as a result from heat added or taken and work performed. 

• Kinetic energy of particles: translational kinetic energy + rotational kinetic energy.

• Heat energy = Thermal energy: "Heat energy that is transferred from one body to another as a result of a difference in temperature until thermal equilibrium".

  • Direction of energy transfer: From body with higher temperature to body with lower temperature.​

 

Thermal concepts and phase changes

• Specific heat capacity (c): "Energy required to increase the temperature of a units mass of a certain substance by one kelvin."

  • Q = mc∆T (always positive!)

  • Thermal capacity (C): "Energy required to raise 1 K of an object (e.g. a container)".​ 

• Specific latent heat (L): "Energy required to change the phase of a unit mass at constant temperature."

  • During a phase change, the temperature does not change, as the kinetic energy does not increase, only the potential energy increases.

  • Q = mL (always positive!)  

• Rate of thermal energy transfer is increased by increasing the difference between the temperatures of a body and that of the surroundings and increasing the surface area.

 

Temperature of a substance changing with time, with energy being supplied by a constant power source:

* Vaporization is different than evaporation - the latter depends on surface area

 

The method of mixtures

• Assumptions: no heat transferred to the surroundings/to the container, substance heated uniformly.

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Pressure

• Pressure (p): "The normal (perpendicular) force applied per unit area." p = Fcosθ/A

  • Units: pascal (Pa) or Nm^-2 .

• Associated with molecules colliding with a container's walls: changing momentum - exerting force per unit area.

Mole​

• A particle can be a single atom (e.g. carbon - C) or be composed of more than one atom, such as oxygen gas (O2 - diatomic) and carbon dioxide (CO2 - triatomic).

  • All single atoms are shown on the periodic table:​

• The unified atomic mass unit (u): "One twelfth of the rest mass of an unbound carbon-12, in its nuclear and electronic ground state, which is  equal to 1.661 x 10^-27 kg." 

  • Protons, neutrons and electrons all taken into account.

  • Atomic mass: "The average mass of an atom in u." Shown on the periodic table.

• Mole (n): "The amount of substance having the same number of particles as there are neutral atoms in 12 g of carbon-12." Unit: mol.

  • One mole has always  6.02 x 10^23 particles = The Avogadro constant (NA)

  • One mole of a mono-atomic substance has a mass in grams equal to the atomic mass in u.

  • Molar mass (u): The sum of the atomic masses of the atoms making up the molecule, e.g. CO2 molar mass = 12 + 2 x 16 = 44 gmol^-1

  • n = N (number of particles)/NA = m(mass)/u(molar mass) = g/g mol^-1.

 

Kinetic model of an ideal gas

A real gas may be approximated to an ideal gas when the density is low, which means at low pressure and high/moderate temperature.

Assumptions in ideal gases:​  

• Molecules are point particles with negligible volume.

• Molecules obey the laws of mechanics.

• No forces between molecules, except in collisions - Only kinetic energy, no potential!

• Duration of a collision negligible compared to time between the collisions.

• The collisions (between particles and from particles on walls) are always elastic

• Molecules have a range of speeds and move randomly.​

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Gas laws

• V = Volume

  • Unit: m³

• Variable 1 means variable at the start of the gas transformation.

• Variable 2 means variable at the of the gas transformation.

The equation of state for an ideal gas

pV = nRT , where R is the gas constant, equal to 8.31 JK^-1 mol^-1                      .

• For constant number of moles: p1V1/T1 = p2V2/T2

 

The Boltzmann equation

• Average random kinetic energy of the particles: EK = 3/2kbT = 3/2 R/NAT

  • The constant kb is known as the Boltzmann constant.

• The total random kinetic energy of all particles, i.e. the internal energy:

  • U = 3/2 NkbT = 3/2nRT = 3/2pV​