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

Conduction Through a Slab

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

Heat Loss Through a Wall

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 = X 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