10/3/20131Lecture 4 (Communication)• Reading Assignment– Density (2.8) – Problem Solving and Dimensional Analysis (2.6)• Questions we’ll answer:– What is density? How does the physical state of a substance determine its density?– How do we efficiently combine measurements in a calculation?• Make sure you have the PDF of these lecture notes printed out before you watch this video!Density: Mass per Unit Volume• For liquids and solids at a fixed temperature, the mass of a substance varies linearly with the volume of the substance.– The situation is a bit more complex for gases, as you’ll learn in 142.• The density of a substance depends on: – composition  mass– temperature  volume.mdVmdVSlope of the line relating mass and volume…d is a constant10/3/20132Density ComparisonsMercury (Hg): 13 g/cm3(liquid at 25oC)Aerogel (silicon dioxide): 2 mg/cm3(Compare to air: 1.2 mg/cm3)Cannonball floats on Hg:http://youtu.be/Rm5D47nG9k4(start at 9 sec)More about aerogel: http://youtu.be/kHnen2nSmDY(start at 19 sec)watericeComposition determines mass.Phase and temperature determine volume.Density and Phaseliquid paraffinsolid paraffin10/3/20133MercuryFreezing point: ‐38oCBoiling point: 357oCMercury remains a liquid for a very broad range of temperatures.Measuring TemperatureWe can exploit the temperature dependence of density to actually measure temperature.• As the volume of the mercury increases, it expands into a narrow capillary tube. • The length of the mercury column indicates the temperature.Examples:1. A block has a volume of 0.253 L. Its mass is 21.7 g. What is the density of the block in g/cm3? 2. Copper has a density of 8.96 g/cm3. A sample of copper is added to 50.0 mL of water in a graduated cylinder, and the levels rises to 83.7 mL. What is the mass of the copper?10/3/20134Dimensional Analysis Examples• The rest of the lecture will be devoted to working through some more dimensional analysis problems.• Conversion factors we might need:Length: 1 m = 1.094 yd 1 mi = 5280 ft 1 ft = 12 in1 mi = 1760 yd 1 Å = 10‐10m 1 in = 2.54 cm (exact)Mass: 1 kg = 2.205 lb 1 lb = 453.6 g 1 dry oz (ounce) = 28.35 gVolume: 1 L = 1.06 qt 1 ft3= 28.32 L1 gal = 3.785412 L1 liquid oz