Chapter 16: Heat Transfer

When we bring two objects together and they are initially at different temperatures, heat will move from the one at a higher temperature to the one at a lower temperature. This will continue until they reach the same temperature. When they are at the same temperature we say they are in thermal equilibrium. There are three primary mechanisms for this heat transfer, Conduction, Convection and Radiation.

(Note that we can make heat flow "backwards" i.e. from the cold object to the hotter one, but some outside agent has to do work on the system to make this occur. It is like water, if left to itself it will flow downhill, but if I intervene and do work on it I can carry it back uphill. Making heat flow "backwards" is the basis of refrigeration, but we have to put in energy to make this occur.)


Conduction

In conduction the heat is transferred from one atom to the next as they collide with each other. In the figure below, the atom on the left initially has more kinetic energy than the others. It collides (pushes and pulls) on the atom next to it and transfers energy to it. The second atom in turn transfers energy to the one to its right as it collides with it and so on until the "extra" energy is shared by all the atoms. (Red represents a lot of KE, pink less, orange even less and green represents the least KE.) Note that the atoms do not move from one end of the chain to the other as the heat is transferred down the chain.

Many of the best conductors of heat are metals (the "free" electrons conduct heat efficiently.) They conduct heat easily and rapidly. Diamond is a surprisingly good thermal conductor, pure diamond is four or five times more conductive than silver even though diamond has almost no free electrons.  Materials that do not conduct heat very well are called insulators. Materials like glass, most plastics, and wood are thermal insulators. Gasses are usually poor conductors (thought they can convect heat quickly).  As a result, materials with lots of small air pockets like Styrofoam and down are very good insulators because the small air spaces inhibit convection so heat must flow by conduction and air is a very good insulator.

The rate of heat transfer or conduction from one point to another depends on several things.

  1. The temperature difference - the greater the temperature difference the faster the transfer
  2. The type of material - the better the conductor the faster the transfer.
  3. The cross sectional area - the larger the area the faster the transfer.
  4. The thickness or distance - the greater the distance, the slower the transfer.

This is a table of the relative conductivities of various materials.

Number 1 above leads to Newton's Law of cooling.  When you have a material with different temperatures on each side, the rate of heat flow through that material is proportional to the temperature difference across the material.  If Thot = 30oC and Tcold = 10oC, the temperature difference is 20oC.  Assume the rate of heat flow is 100J/s.  If the temperatures are changed the rate of heat flow will also change.  Say Tcold changes to 0oC.  Now the temperature difference is 30oC.  The rate of heat flow will change by a factor of the ratio of the two differences, or the new flow rate will be (30/20) times the old flow rate, or 150J/s.  This is exact for conduction, but is approximately true in other situations as well, i.e. when some of the heat transfer is due to convection and radiation.

Conduction is usually slow at transfering heat over long distances, see #4 above.  


Convection

This is a mixing process, and as a result it is confined to liquids and gasses. The atoms move from one location to another and carry the heat with them. This mixing motion of atoms is due to buoyancy. If I heat a gas, it will expand and become less dense. If it is less dense than the gas surrounding it, it will rise because the buoyant force pushing it up is greater than its weight. This motion produces the mixing and the consequent transfer of thermal energy (flow of heat).

For convection to occur in a room of air, you need to heat the air near the bottom of the room.  That warmed air will expand, become less dense and be pushed up by the buoyant force exerted on it by the surrounding gas.  

If you heat the air at the top of the room, that air will expand and become less dense and stay at the top and you will not have the mixing that would result from heating the air at the bottom of the room.  

Many liquids are poor conductors of heat and most gasses are insulators, i.e. thermal insulators, and heat transfers over large distances in these materials usually involve convection. This is especially true in gasses like air. We depend on convection to transfer heat in our houses.  


Radiation

This refers to electromagnetic radiation, traveling electric and magnetic fields that can move through empty space carrying energy. This energy comes in bundles called photons. Electromagnetic radiation is often classified by how energetic the photons are.

Note that visible light is only a small part of the electromagnetic spectrum.  (In the above diagram, lower frequencies are at the left and higher frequencies are on the right; the higher the energy per photon, the higher the frequency.)  

All objects above 0K (absolute zero) emit electromagnetic radiation because of the thermal motion of their atoms. Thus they are emitting energy in the form of electromagnetic radiation. The higher the temperature, the more energy they emit per second (i.e. power). Also the energy per photon increases with temperature. We are not too hot (about 300 – 310 K) so we emit infrared radiation. The sun is much hotter (the surface is around 5800K) and emits visible light along with some ultraviolet and infrared. The energy we receive from the sun comes from radiation.

We also adsorb radiation emitted by other objects near us. If we are warmer than the walls of the room around us, we transfer more heat to the walls by the radiation than we receive from the walls, providing a net transfer of heat to the walls. If we are cooler than the walls we will receive more than we emit, thus gaining energy.  

Some objects are good at absorbing radiation while others are not.  Good absorbers are also good emitters of radiation and poor absorbers are poor emitters.  A perfect absorber is called a blackbody and absorbs all the radiation striking it.  White objects tend to reflect radiation rather than absorbing it, that is they are poor absorbers.  However poor absorbers are also poor emitters, and white objects are poor emitters of radiation.

If you are in the sun and wear black clothing, your clothing will absorb the light (and its energy) and warm up.  If you wear white clothing, it will reflect the light rather than absorb it. It will not warm up as fast.  White snow reflects most of the light and as a result it warms up more slowly on a sunny day than snow that has dirt or other debris on it that makes its surface darker..

Two things determine the average temperature of the earth. The first is the rate at which we receive energy from the sun. The second is the rate we radiate energy away. The balance between these two determines the temperature of the earth.  On the daytime side of the earth, we typically  receive more radiant energy from the sun than we radiate away and the daytime side of the earth warms up.  On the nighttime side, we radiate more energy away than we receive and we cool down.