(wed class begin by finishing material that is posted to the Web for Monday)

Additional topics for today: Heat calculations

• heat capacity
• heat of phase change
• crystal lattice

Demonstration in class-- Liquid Nitrogen

• temperature -195 C or 78 K
• fairly ordinary liquid otherwise
  • water like density, viscosity
  • clear, colorless
• but it is really normally at its boiling point
• will stay at bp, evaporation absorbs the heat
• slowly bubbling, faster if near heat
  • (the whole world is heat)
• clouds are water vapor, condensed by cold N₂ gas

Rubber Phase Transition

• small "superball"
  • cooled to -195^oC
    • bounces pretty well (80% rebound)
• warms over about 2 minutes in room air
  • in about 1 minute
    • temp is about -90^oC
    • bouncing abruptly changes
    • now <10% rebound (dull thud)
• in another minute
  • ability to bounce is restored
• At -195^oC one solid (crystal lattice) exists
  • it's hard and rigid
  • but will bounce
    • actually steel and solid glass balls bounce well
• at -90^oC a new solid phase forms
  • this is different
  • bounces more like simple putty
• at warmer temperatures
  • that phase disappears
  • is replaced with the usual bouncy rubber

Heat Capacity

• heat = (heat capacity) x D Temperature
  • units-- heat in Joules , heat_capacity in Joules/K (or ^oC) and deltaT in K (or ^oC)
    • text varies, K or ^oC
    • also my DTtemperature is delta-Temperature
  • usually heat capacity is given per gram or per mole
    • we want capacity of actual sample
    • multiply by #g or #moles

• water -- molar heat capacity is 75.4 J/mol ^oC

• let's explore a 250 ml glass of water
  • density 1.0 g/ ml (250 g)
  • formula weight is 18.0 g/mol
  • so # moles = 250./18.0 = 13.9 moles

• sample heat capacity is 13.9 mol x 75.4 J/mol ^oC
  • that's 1048 J/ ^oC

• assume it takes 6 minutes for ice drink (no ice, but 0^oC) to warm to 15^oC (cool)

• # Joules = 1048 (J/^oC) x 15 (^oC)= 15720 J
• heating rate is 15720 J / 360 seconds = 43.7 J/sec

• How would 250 g of ice behave at that heating rate?

• heat comes in at same 43.7 J/sec
• task now is to melt 250 g of ice (13.9 mol)
• DH_fusion = 6.01 kJ /mol
• need 6.01 x 10³ Joules/ mol x 13.9 mol = 83539 J

• time = 83539 J /43.7 J/sec = 1911 seconds = 32 minutes
• (we'd still need another 6 minutes to get to 15^oC again)

• Conclusion?
  • Ice is much better refrigerant than cold water

Crystal Lattice, Structure

• First, how do you determine the fine structure?
  • eyes and normal microscopes can't see atoms
  • (we can now, but our knowledge is older)
• Atomic theory is logical
  • visible crystals are have well formed edges
  • definite shapes but variable size
  • repeating fine structure
  • key phrase is actually "long range order"
• One of the best tools is X-Ray Diffraction
  • go back to Friday's lab and Diffraction Grating
    • dispersed light to form spectrum
    • light is electromagnetic wave
    • has wavelength (500 nm = green light)

• wave (500) -------------> \ -------a-------- / ----a+b--->
  • (sorry but the Web notes won't show this figure well-- mirrors split and recombine the beam of light)

• path 2 is longer and waves (a+b) out of synch

• ½ wavelength, destruction of light
• if difference is 1 wavelength, you see brightness
  • optical interference

• grating is more complex (many equally spaced reflectors)
  • but same idea
  • at most angles green light vanishes
  • further on it appears brightly
  • then further on it vanishes
• With white light
  • each color has angle where it appears
  • vanishes at other angles
  • so we see colors spread out as a spectrum
• Requires line spacing be about the wavelength of light
  • 500 nm spacing
  • 1 / 500 x 10^-9 m = 2 x 106 lines per meter 2000 line/mm

X-ray diffraction is similar

• we use one wavelength
• reverse the logic... use angle to determine spacing
  • want to measure atomic spacing
  • 0.1 nm typically
  • so we need wavelength of 0.1 nm
  • that's X=rays
• Pattern is that of a 3-D grating
  • can determine 3D placement of atoms
  • (actually spacing of repeating atoms)

Crystal lattice and Unit Cells

• don't need to memorize details
  • should recognize cubic and face centered cubic
• should feel comfortable with concepts
• be able to count atoms per cell from a picture

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