Topic 3: Thermal Physics
3.1 Thermal Concepts
Particle model of matter
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Macroscopic world VS. microscopic world
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Matter is consisted of small structures: Molecules...Atoms...Quarks, known as Particles.
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Inter-particle forces: "Spring-like" bonds between particles.
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Bond force: Solid (s) > Liquid (l) > Gas (g) - phases of matter.
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Absolute temperature
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"Absolute temperature is proportional to the average random kinetic of the molecules".
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Absolute temperature = T (in kelvin, K) = Temperature in degrees Celsius (ºC) + 273
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Absolute zero (0 K): Zero Kinetic energy (theoretically).
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Triplet point of water (273 K): water can be in any of the 3 phases.
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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.
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Kinetic energy of particles: translational kinetic energy + rotational kinetic energy.
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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".
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Direction of energy transfer: From body with higher temperature to body with lower temperature.
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Thermal concepts and phase changes
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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!)
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Thermal capacity (C): "Energy required to raise 1 K of an object (e.g. a container)".
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Specific latent heat (L): "Energy required to change the phase of a unit mass at constant temperature."
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During a phase change, the temperature does not change, as the kinetic energy does not increase, only the potential energy increases.
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Q = mL (always positive!)
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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
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Assumptions: no heat transferred to the surroundings/to the container, substance heated uniformly.
3.2 Modelling a Gas
Pressure
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Pressure (p): "The normal (perpendicular) force applied per unit area." p = Fcosθ/A
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Units: pascal (Pa) or Nm^-2 .
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Associated with molecules colliding with a container's walls: changing momentum - exerting force per unit area.

Mole
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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).
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All single atoms are shown on the periodic table:
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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."
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Protons, neutrons and electrons all taken into account.
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Atomic mass: "The average mass of an atom in u." Shown on the periodic table.
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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.
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One mole has always 6.02 x 10^23 particles = The Avogadro constant (NA)
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One mole of a mono-atomic substance has a mass in grams equal to the atomic mass in u.
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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
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n = N (number of particles)/NA = m(mass)/u(molar mass) = g/g mol^-1.
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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:
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Molecules are point particles with negligible volume.
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Molecules obey the laws of mechanics.
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No forces between molecules, except in collisions - Only kinetic energy, no potential!
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Duration of a collision negligible compared to time between the collisions.
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The collisions (between particles and from particles on walls) are always elastic
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Molecules have a range of speeds and move randomly.
Gas laws
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V = Volume
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Unit: m³
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Variable 1 means variable at the start of the gas transformation.
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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 .
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For constant number of moles: p1V1/T1 = p2V2/T2
The Boltzmann equation
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Average random kinetic energy of the particles: EK = 3/2kbT = 3/2 R/NAT
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The constant kb is known as the Boltzmann constant.
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The total random kinetic energy of all particles, i.e. the internal energy:
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U = 3/2 NkbT = 3/2nRT = 3/2pV
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