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Phy 202: General Physics II

Phy 202: General Physics II. Ch 13: Heat Transfer. Jean Baptiste Fourier (1768-1830). French mathematician Originally wanted to become a priest but drawn to mathematics Contemporary of Laplace, Lagrange, Biot & Poisson Served as Precept under Napoleon Worked on: mathematics

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Phy 202: General Physics II

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  1. Phy 202: General Physics II Ch 13: Heat Transfer

  2. Jean Baptiste Fourier (1768-1830) • French mathematician • Originally wanted to become a priest but drawn to mathematics • Contemporary of Laplace, Lagrange, Biot & Poisson • Served as Precept under Napoleon • Worked on: • mathematics • heat conduction • Yesterday was my 21st birthday, at that age Newton and Pascal had already acquired many claims to immortality.

  3. Types Heat Transfer • Convection • Heat energy that is carried from place to place by the bulk movement of a fluid • Conduction • Heat energy that is transferred directly through a material • Radiation • Heat energy that is transferred by means of electromagnetic waves (radiant energy or light)

  4. Conduction • Heat flow due to collisions between neighboring atoms (a sort of “domino effect”) • The rate of conductive heat flow (Q/Dt) is: • proportional to temperature difference between 2 regions in a conducting pathway material (DT) • proportional to cross sectional area of material (A) • proportional to ability of material to conduct heat (k) {called thermal conductivity} • inversely proportional to length of conducting pathway (L) • Combining all of these elements forms Fourier’s Heat Equation (1609): Q/Dt = k (A.DT) / L (Rate of Heat Flow in W) Or Q = [k (A .DT) / L] .Dt (Heat Flow in J)

  5. Conduction depends on temperature difference between 2 regions & how far apart those regions are separated Increasing the cross-sectional area increases amount of heat that will flow in a given time Conductive Heat Flow • Of course, the relative ability to conduct heat is an intrinsic property of different materials !!

  6. Convection • When a fluid is warmed: • Volume expands (thermal volume expansion) • Density decreases • Buoyant forces exerted by cooler (denser) fluids causes warmer fluids to rise • Remember Archimedes’ Principle ??? • As warmer fluids rise they cool and descend warmer fluids beneath push them out of the way • The net result is a natural mixing that occurs, called convection • Convection is a very efficient form of thermal transfer • Heat energy gets rapidly dispersed throughout the bulk of a fluid • When mixing is induced artificially (i.e. with a fan) convection occurs more rapidly & efficiently, this is called forced convection

  7. Convection Currents in heating & cooling appliances Convection currents in a saucepan Examples of Convection

  8. Radiation • All objects emit(or radiate) energy in the form of electromagnetic waves • The rate of radiant energy emitted is related: • Surface area (A) • The 4th power of the surface temperature (T4) {in kelvin!!} • The ability of an object absorb/emit radiant energy, called emissivity (e) e is 0 for a perfect reflector e is 1 for a absorber/emitter e is between 0 & 1 for normal substances and varies with wavelength • Combined together we have Stefan-Boltzmann’s Law of Radiation: Q/Dt = e (s A.T4) (Rate of Radiant Heat Flow in W) where s = 5.67 x 10-8 J/s.m2.K4(the Stefan-Boltzmann Constant)

  9. Effect of Emissivity on Absorption of Radiant Energy • All bodies emit as well as absorb radiant energy • When a body is in thermal equilibrium: Qabsorbed = Qemitted • Dark objects will reach higher equilibrium T than lighter objects (e.g. consider pavement and concrete on a hot day!) • Good emitters are also good absorbers of radiant energy (e ~ 1) • Poor emitters are also good poor of radiant energy (e ~ 0)

  10. The Greenhouse Effect • The presence of our atmosphere helps the Earth maintain a moderate & livable temperature range, due to a process called the Greenhouse Effect: • Radiant energy (short wavelength) from the sun is absorbed by the surface of earth • The earth’s surface radiates energy (long wavelength) • Some of the long wavelength radiation is reflected by the earth’s atmosphere by so called “Greenhouse Gases” • The reflected long wavelength radiation is reabsorbed by the earth’s surface • This positive feedback process heats the surface of the earth and keeps the surface warmer at night • Do not confuse Greenhouse Effect (Good!) with Global Warming (Bad!) • Global warming is believed to be due to an increased production of greenhouse gases which may increased the amount of long wavelength radiation reflected back to the Earth

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