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.

Interparticle forces: "Springlike" 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 intermolecular 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

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 carbon12, 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 carbon12." Unit: mol.

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

One mole of a monoatomic 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 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
