Essay on Heat Transfer on a Microscopic Scale

There are three primary modes of heat transfer: convection, conduction, and radiation

There are three primary modes of heat transfer: convection, conduction, and radiation. Briefly stated, convection is groups of atoms with a different density that displace other groups of atoms in a gas or liquid. Conduction is where atoms jiggle around in place and transfer their heat to neighboring atoms, and radiation is when rays of light collide with atoms to increase their jiggly motion.

Convection is the simplest form as it’s atoms moving around a substance and carrying their internal energy with them. Convection typically happens on a macroscopic scale where you have currents of a liquid or gas that are at a different temperature than the rest of the gas moving around. Collections of particles at a higher temperature than their surroundings are less dense because of their higher velocities. The higher velocity of each individual particle causes them to push particles they bounce off of farther away and this excess vibrational force is what causes the lower density. For example, when heating up a pot of water, particles at the bottom of the pot will have higher energy than particles at the top and therefore they will be less dense. This will cause the particles at the bottom to move towards the top of the pot. The cool particles at the top of the pot will then be displaced by the warmer particles causing convection currents. The same convection phenomena occur in both gases and liquids.

A natural question may be, “How do the particles toward the bottom of the pot get this excess heat?” Well, the obvious answer is from the flame on the stove, but how does heat get transferred on a microscopic level from a flame to a pot, and from a pot to water? In the case of a propane stove, C3H8 reacts with O2 to form CO2 and H2O plus heat. This means that the carbon dioxide and water are highly energized and because they are highly energized they bump into O2 and C3H8 molecules hard enough to cause them to react. This is the chain reaction that creates fire. Those molecules then bump into the bottom of the pan and transfer heat to those molecules. Within the pan is where conduction takes place.

Conduction occurs when two or more objects come into contact with each other or inside of a single object when units of energy randomly disperse. There are two primary particles (or quasi-particles) responsible for conduction: electrons and phonons. Let’s talk about phonons first since they’re the least intuitive. Jess Gwynne summed phonons up best with the following quote: “A phonon is a quantum mechanical adaptation of normal modal vibration in classical mechanics” [1].

In non-metals, the primary method for heat to be transferred is phonons. Since phonons are the quantization of atom vibrations in a solid or liquid it makes sense that although phonons and electrons exist in both metals and nonmetals electrons dominate when they can hop from one atom to the next. Intuitively speaking anytime there is movement of mass from one location to another that is the fastest way to transfer heat. This is analogous to convection being faster at transferring heat than conduction. A phonon is analogous to a photon, but instead of an electromagnetic excitation, it’s a thermal vibration. The energy of a given lattice fibration is quantized into the phonon quasiparticle. The energy of a phonon is proportional to its angular frequency omega.

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Here n is the quantum number, and the term undefined is the zero point energy of the mode.

In a metal, the predominant mode of thermal conduction is through electrons. Electrons are the carriers of both heat and electricity. In fact, there is a relationship between the two and it’s called the Wiedemann-Franz law.

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Here, L is the proportionality constant, κ is the thermal conductivity and σ is the electrical conductivity. Since L has to stay constant as kappa increases sigma must also increase to maintain the same proportion. This means that if a metal has a higher thermal conductivity it will also have a higher electrical conductivity. Intuitively this makes sense being that most metals conduct heat quite well. You would never insulate your house with a metal roof. And, the best insulation is styrofoam; a very poor conductor. The movement of these electrons can be modelled simply using Drude’s theory. The Drude model simplifies things by using classical mechanics and assuming that all nuclei are fixed. It also assumes that electrons move in a straight line and don’t interact with each other. A depiction of this model can be seen in Figure 1. In the figure red indicates heat. There is a heat source to the left and a heat sink to the right. A small red hallo can be seen around the electrons to depict the heat that they carry with them when they move from atom to atom.

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Figure 1. Drude model of heat transfer by electron movement

Heat always moves from a higher temperature to lower temperature because of entropy. The second law of thermodynamics states that the entropy of the universe always increases. It can, however, stay the same if there is a reversible process. The reason this law comes about is statistical in nature. If there are 10 places that 10 units of energy can be located in and all those locations are equally likely then it is much more likely to find the energy evenly spread out than to find all 10 units of energy in a single location. Therefore, entropy is one of the strongest explanations for why heat moves from hot to cold.

The final mode of heat transfer is radiation. All objects radiate light. This is called blackbody radiation. Even an object at room temperature radiates light, but it’s out of the visible spectrum. The frequency of radiation depends on the object temperature. As an object heats up the frequency increases toward the visible range and beyond. This is why heating up metal or glass turns it bright orange. It’s also why fire is orange. In the example above electrons in higher energy orbital falling back down to lower energy orbitals are responsible for some of the visible light of the fire, but in “dirty” fires much of the visible light is from blackbody radiation. This is what transfers heat between two objects when there is no conduction or convection between them. It’s how the sun transfers heat to the earth.

Heat transfer at a microscopic scale is most easily understood through classical mechanics, but it doesn’t do the best job explaining everything we see. Therefore, a more intricate explanation is required to truly understand what is going on. But, to get an intuition for what is going on on the atomic level, classical mechanics does quite well. It explains how heat transfers through conduction by describing it as electrons and atoms bouncing around. It describes convection as atoms rising and falling due to density differences and displacing atoms of different densities. And, it explains radiation on a surface level by describing them as beams of light that bounce into atoms and move them around.

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