The subject of thermodynamics depends on some parameters.
Thermodynamic temperature is one of them.
It describes the absolute measure of temperature.
We are used to thinking of temperature by thinking of comparisons.
We say something is hot or cold relative to some [sometimes physical] reference.
Thermodynamic temperature is different, however.
It is an absolute measure of the average total internal energy of an object–the energy of motion (kinetic energy) and energy because of other factors.
What’s in a name?
The reason thermodynamic temperature is also called absolute temperature is that:
1. it does not depend on the peculiar properties of a particular material;
2. it refers to an absolute zero according to the properties of the ideal gas.
Thermodynamic temperature is based on the third law of thermodynamics.
This law highlights the null or zero point as the theoretically lowest temperature.
Particles of matter at absolute zero have a minimal motion and cannot become colder.
This is the state of lowest energy.
It applies to the mean (average) energy of a mass of atoms or subatomic particles.
These may be atoms in a bar of iron.
It may also refer to air molecules in a confined space.
It is measured as a number of kelvins above absolute zero– in theory, it is the coldest point anything can be.
Kinetic energy is highest when an object moves through space–translational motion.
Thermal energy diffusion
Thermal energy diffusing from hot regions of a system to cold is how heat conduction happens.
A system can be one bulk entity or many discrete bulk entities.
Bulk refers to a statistically significant amount of particles.
This can be a microscopic amount.
Each time thermal energy courses through any isolated system, temperature differences in the system is zero, while entropy (randomness) increases.
The particular motion responsible for temperature is translational motion.
One type of heat conduction mechanism happens when translational motion transfers momentum (an acceleration of particles) from particle to particle via numerous collisions.
Gases have atoms or molecules scurrying in many directions, inevitably colliding with each other and any available barriers.
In gases, momentum (heat) diffuses throughout the volume of the gas through serial collisions.
However, entire molecules or atoms can move forward into new territory, taking their kinetic energy with them.
The molecules have varying individual speeds, but there is mostly a central speed to which most tend to.
Thus, temperature differences equalise throughout gases quickly, particularly where light atoms or molecules are involved.
Convection hastens the process even more.
The energy content of atoms and molecules determines their speed.
How about solids?
Solids are made of atoms with limited freedom of movement.
The atoms cannot move independently.
This results from tight covalent bonds.
The kinetic energy manifests in the form of collective motions called phonons.
This means that translational motion in solids takes the form of phonons.
Phonons are quantized wave packets, with little room to move.
They travel at the speed of sound of the substance involved.
Heat energy also flows through solids in the motion of unbound, mobile electrons.
The pattern of phonon interaction within a solid confers key properties to the solid.
Thermal conductivity is one of these properties.
In solids that are good electrical conductors, phonon-based heat conduction is often inefficient.
Examples of solids with good thermal insulation properties include glass, rock, rubber, and ceramic.
They are great thermal insulators because the solid atoms and molecules are locked in place against their neighbours with little freedom to roam.
Metals, however, are not restricted to only phonon-based conduction.
Heat energy moves through metals swiftly because of direct molecular collisions.
Most of the thermal energy is mediated through light, mobile conduction electrons.
Vibration and rotation are forms of kinetic energy in complex objects.
These contribute to the total energy content.
Thermodynamic temperature is in proportion to the mean of all the energies in all the ways in which it is possible for an object to move–translation, vibration, and rotation.
These are the degrees of freedom of an atom of the object.
To illustrate, an atom of the element helium has only 3 degrees of freedom.
1. motion in the up-down direction
2. motion in the left-right direction
3. motion in the back-forth direction
For those familiar with the idea, these correspond to x, y, and z-axes.
Now, take a nitrogen molecule.
It has two atoms.
This adds two additional degrees of freedom–one rotational and the other vibrational.
The more components there are in a complex object, the greater the number of possible motions and degrees of freedom.
Measuring the internal energy of particles
Measuring this internal energy of objects presents great difficulty.
Scientists measure the thermal energy emitted as the particle moves to or from a system of objects and a thermometer until a state of thermal equilibrium occurs–no heat flows between them.
What they measure here is temperature.
Internal energy and temperature are separate entities.
They are, however, directly related.
Energy is measured in joule, a derived SI unit that is itself an aggregate unit of three fundamental SI units–the kilogram (kg), the metre (m), and the second (s).
Thermodynamic temperature, however, is measured in Kelvin.
How to connect joule (J) and Kelvin (K)
To bridge internal energy and thermodynamic temperature, scientists use the Boltzmann constant (kB or k).
It relates the kinetic energy content (E) of matter to its temperature (T).
Thus, E = kBT
At the most basic level, taking the simplest collection of particles (atoms), the kinetic energy is represented as ½mv2 distributed over three degrees of freedom.
m represents mass, while v is the velocity.
Thus, the total translational energy is 3/2kBT.
At equilibrium, each degree of freedom (a way to store internal energy) will have on average the same energy–kBT/2.
Remember, kB is the Boltzmann constant.
The thermal conduction properties of solids and gases are given serious consideration in the production of temperature-controlled vehicles sold by Glacier Vehicles.