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 Q 1 = (333000)(0.02) = 6660 J  Heat 2: warm up now melted ice cube Q 2 = (4190)(0.02)(T f -0)  Heat 3: cool down tea Q 3 = (4190)(0.3)(T f -90)  Step 4: add up heat Q 1 + Q 2 + Q 3 = T f T f – = T f = T f = 79.4 C

Water condenses out of the air onto a cold piece of metal. Due to this condensation, the temperature of the air around the metal, A)Increases B)Decreases C)Stays the same D)Fluctuates unpredictably E)It depends on the temperature of the metal

Ten joules of heat are added to a cylinder of gas causing the piston at the top to rise. How much work does the piston do? A)0 Joules B)5 Joules C)10 Joules D)-10 joules E)You cannot tell from the information given

Which of the processes in the diagram produces the least work? A)1 B)2 C)3 D)4 E)All are the same

Which of the processes in the diagram involves the least heat? A)1 B)2 C)3 D)4 E)All are the same

Heat Transfer  How is heat transferred from one place to another?  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   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 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  For Al, k=235 for Cu, k=428 (W/ m K)    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

Heat Loss Through a Wall

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  Where  is the Stefan-Boltzmann constant = X W/m 2 K 4   T must be in absolute units (Kelvin)

Absorption of Radiation  P a =  AT env 4   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   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

Today’s PAL a)Consider a house window with a size of 1 meter by 1.5 meters and 0.75 cm thick. Inside the house it is 20 C and outside it is 10 C. Compare the heat loss through the window by both conduction and radiation. Which is greater? b)Imagine you replace the window with a double-pane window composed of two 0.25 cm thick windows with 0.25 cm of air in between. What is the heat loss rate due to conduction now?

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

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 

Next Time  Read:  Homework: Ch 18, P: 54, 57, Ch 19, P: 5, 7, 19