Topic 3: Thermal Physics

3.1 Thermal Concepts

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.

3.2 Modelling a Gas


  • 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.



  • 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 particlesThe 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.

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 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 kis 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​