Basic Definitions:
Absolute temperature (Kelvin) is defined as the random, average translational kinetic energy of the atoms or molecules within a substance. Not, the KE of the object itself. That is, if an ice cube is traveling at 3 m/sec and has a mass of 1 kg, it has a translational KE of ½(1)3^{2} = 4.5 J, that KE does not represent its temperature. Its temperature is represented by the statistical average translational KE of an ice molecule within the cube, KE_{molecule} = ½mv_{rms}^{2} where v_{rms} represents the root mean square velocity of a random molecule within the ice's lattice structure. That velocity would be very small since the temperature of ice is 0ºC or 273 K. There are three primary temperature scales: Kelvin, Centigrade, and Fahrenheit.
Internal energy is the total energy of all the molecules within a substance; the sum of their average translational kinetic, rotational kinetic and potential energies. All of these energies are measured on the molecular level, not based on what the "gross large scale" object is doing. Compared to an iceberg, a cup of hot water has a much higher temperature but a much smaller total internal energy. An object's internal energy is sometimes refered to as its thermal energy.
Heat is the transfer of internal energy from one object to another. Heat flows from objects at high temperatures to objects at lower temperatures and ceases when they reach the same temperature.
Heat Transfer Methods:
Three means by which heat is transferred from one location to another are: convection, conduction, radiation
Convection means that the actual particles circulate from one location to another. This is the type of heat transfer you think about when you say that hot air rises and cold air sinks.
Conduction is when the heat is transferred through a material by the collisions of adjacent atoms or molecules. Heat always flows from high temperatures to low temperatures. This is analogous to the fact that charged particles always flow from positions of high potential to those of low potential. The formula used to calculate the rate at which heat is conducted through a solid from its warmer side to its cooler side is
- k is the coefficient of conductivity is measured in W/Km
- ΔQ/t is called the heat current (J/sec or watts)
- ΔT is the temperature differential (K)
- A is the cross-sectional area (m
^{2})
- ΔL is the length or thickness of the material (m)
The importance of this formula is that the amount of heat conducted is directly proportional to the temperature gradient and the conductor's cross-sectional area and is inversely proportional to the conductor's length. For example, if the metal bar shown in the diagram were to be doubled in length, the heat current would be cut in half since ΔL would be doubled. If the temperature of the heat source (in Kelvin) were to be tripled, the heat current would also be tripled since ΔT would be tripled. If the radius of the conductor were to be doubled, the heat current would be quadrupled since the area of a circle equals π r^{2}. Conductivity is also the reason why different materials at "the same temperature" seem to feel warmer or cooler when touched. A wooden table surface, which has a low coefficient of conductivity (0.08 W/Km), seems to feel warmer than an silver tray, which has a high coefficient of conductivity (430 W/Km), resting on its surface. Both are at room temperature, but the metal conducts heat away from your hand more quickly and therefore "feels" cooler. When the heat current (ΔQ/t) has to pass through multiple layers of materials having different coefficients of conductivity, our formula becomes,
The ratio L/k is called the R value for each layer and is used as the means of rating insulation. Let's practice using these conductivity formulas before examining the basic principles and formulas for radiation. |