Heat Transfer Physics 202 Professor Lee Carkner Lecture 14

PAL #13 First Law  Final temperature of 20 g, 0 C ice cube dropped into 300 g of hot tea at 90 C.  Add up all heats (Q = cm  T and Q = Lm)  Heat 1: melt ice  Heat 2: warm up now melted ice cube  Heat 3: cool down tea  Step 4: add up heat T f T f – = T f =

Heat Transfer   What is moving?   In heat transfer the analogous methods are convection and conduction   both a particle and a wave (but not really)

Conduction   The end in the fire experiences a large vibration of the molecules of the metal    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 H = Q/t = kA (T H - T C )/L  Where:   Q is heat and t is time   A is the cross sectional area of the material (in the direction of heat transfer)   T is the temperature (hot or cold)

Thermal Conductivities  Metals generally have high k   Al and Cu make good pots and pans   For air, k=0.026 for polyurethane foam, k=0.024   Down filled winter coats trap air for insulation

Composite Slabs  H = Q/t = 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

Conduction Through Multiple Layers

Heat Loss Through a Wall

The Surface of the Sun

Convection  Hot air (or any fluid) expands and becomes less dense than the cooler air around it   If the hot air cools as it rises it will eventually fall back down to be re-heated and rise again   Examples: baseboard heating, boiling water, Earth’s atmosphere

Convection Rate Factors  Fluidity   Energy exchange with environment   How rapidly will the material lose heat?   A small temperature difference may result in not enough density difference to move

Radiation  Energy can be directly transported by photons   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   Emissivity has a value between 0 and 1

Absorption of Radiation  Every object also absorbs radiation at a rate determined by its properties and the temperature of its environment  Where T env is the temperature of the environment  P n = P a -P r =  A(T env 4 - T 4 )

Blackbody Radiation   They absorb all of the radiation incident on them   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

Structure of the Sun Core Radiative Zone Convective Zone Photosphere Chromosphere Corona

Heat Transfer in The Sun   Near the core (where the energy is produced via hydrogen fusion) energy is transported by radiation   About 75% of the way out, the opacity increases to a level where convection becomes dominant   Convection transports the energy to the surface where it radiates away into space 