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:

phasechange.png

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

  • 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:​

Periodic_table_large.png
  • 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.

GasLaws.png

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​

ib-physics.net is a student initiative to provide free material to help international students prepare for the IB exams.

For any feedback or comments, contact a fellow IB alumni:

Maria Eduarda Lopes | mariaticilopes@gmail.com

Disclaimers: the IB organization does not endorse this website's content.

All images are under copyright that allows them to be shared.

(the source and copyright details may be downloaded by clicking on the images)