Heat Transfer Physics 202 Professor Lee Carkner Lecture 12

PAL #11 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

Heat Transfer   What is moving?  In mechanics energy can be transferred through a particle (e.g. a bullet) or a wave (e.g. a sound wave)   Heat can also be transferred by radiation  both a particle and a wave

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

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   For Al, k=235 for Cu, k=428 (W/ m K)   Materials with low k are good thermal insulators   We use foam to insulate our houses  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

Radiation   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   T must be in absolute units (Kelvin)

Absorption of Radiation  P a =  AT env 4  Where T env is the temperature of the environment  P n = P a -P r =  A(T env 4 - T 4 )

Emissivity  What is the value of emissivity?    Objects with an emissivity of 1 are called blackbody emitters or absorbers   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   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   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

Next Time  Test #2  For Monday January 9:  Read:  Do Webassign homework

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 change in internal energy? A)1 B)2 C)3 D)4 E)All are the same

Which of the processes in the diagram must have net heat output? A)1 B)2 C)3 D)4 E)3 and 4

Which of the processes in the diagram must have net heat input A)1 B)2 C)3 D)4 E)1 and 2