Heat Transfer How is heat transferred from one place to another? What is moving? In mechanics energy can be transferred through a particle (e.g.
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Heat Transfer How is heat transferred from one place to another? What is moving? In mechanics energy can be transferred through a particle (e.g. a bullet) or a wave (e.g. a sound wave) In heat transfer the analogous methods are convection and conduction Heat can also be transferred by radiation both a particle and a wave (but not really)
Conduction If you place one end of a metal bar in a fire the other end get hot The end in the fire experiences a large vibration of the molecules of the metal These molecules bump into adjacent molecules passing the energy up the bar This is called conduction The movement of heat from a high temperature region to a low temperature region through another material
Conductive Heat Transfer The rate at which heat is transferred by conduction is given by dQ/dt = kA (T H - T C )/L Where: H is the rate of heat transfer Q is heat and t is time k is the thermal conductivity (in W/ m K) A is the cross sectional area of the material (in the direction of heat transfer) L is the thickness of the material T is the temperature (hot or cold)
Thermal Conductivities Metals generally have high k For Al, k=235 for Cu, k=428 (W/ m K) Al and Cu make good pots and pans Materials with low k are good thermal insulators For air, k=0.026 for polyurethane foam, k=0.024 We use foam to insulate our houses Down filled winter coats trap air for insulation Consider touching air, wood or metal at the same temp – metal feels coldest because it carries heat away from your hand the fastest.
Composite Slabs To find the heat transfer through a composite slab made of several materials you need to know the thermal conductivity and the thickness of each dQ/dt = A (T H - T C )/ (L/k) Where (L/k) is the sum of the ratios of the thickness and thermal conductivity of each layer of the slab
Radiation Energy can be directly transported by photons This is how you are warmed by sunlight The power (in Watts) that is emitted by an object depends on its temperature (T), its area (A) and it emissivity ( ) P r = AT 4 Where is the Stefan-Boltzmann constant = 5.6703 X 10 -8 W/m 2 K 4 Emissivity has a value between 0 and 1 T must be in absolute units (Kelvin)
Absorption of Radiation Every object also absorbs radiation at a rate determined by its properties and the temperature of its environment P a = AT env 4 Where T env is the temperature of the environment Any object thus has a net energy exchange rate with its environment of: P n = P a -P r = A(T env 4 - T 4 )
Blackbody Radiation Objects with an emissivity of 1 are called blackbody emitters or absorbers They absorb all of the radiation incident on them Objects that are dark in color absorb more radiation than light objects (have larger ) Every object whose temperature is above 0 K emits thermal radiation People emit thermal radiation at infrared wavelengths and thus can be detected at night with IR goggles
Convection Hot air (or any fluid) expands and becomes less dense than the cooler air around it The hot air is thus lighter and rises If the hot air cools as it rises it will eventually fall back down to be re-heated and rise again This is called a convection cell Examples: baseboard heating, boiling water, Earth’s atmosphere
Convection Rate Factors Fluidity Material must be free to move Energy exchange with environment How easy is it to heat (by conduction or radiation) the material in the first place? How rapidly will the material lose heat? Temperature difference A small temperature difference may result in not enough density difference to move
Greenhouses and the Greenhouse Effect Greenhouses prevent heat from escaping from near the Earth’s surface By preventing convection Greenhouse gases in the greenhouse effect slow heat from escaping from near the Earth’s surface By slowing radiation
1 st Law of Thermodynamics The energy of an object can be changed by Work or heat We will consider only changes in the object internal energy Internal energy = total microscopic kinetic and potential energy of the atoms and molecules making up the object It does not include kinetic energy of the center of mass nor the potential energy due to the position of the center of mass 1 st Law: E int = Q-W by Q is + if heat is absorbed by object, - if heat is given off by object W by is + if work is done by object, - if work is done on object