Continuing with units of measure - density and heat capacity
"Which weighs more - a pound of feathers or a pound of lead?"
Feathers have more volume, but a pound is still a pound.
Mass is an extrinsic property in that it depends on how much we have. Better for comparison are instrinsic properties that depend only on what the material is.
Density - physical property that relates the mass of an object to volume.
typical unit (non-SI) - g / cm3 = g cm-3 = g / ml = g ml-1
DEMO: Comparing densities of gases Halocarbon 4.15 g / L, O2 - 1.3 g/L, H2 0.081 g / L, He 0.2 g /L (note unit change)
Many are temperature dependent - in particular, the density of a gas changes a lot with temperature whereas the density of solids and liquids to not change as sharply.
DEMO: show w/ gas in LN2
"Helium is lighter than air" - We really mean helium is less dense then air.
Note: Ice is less dense than water, ice floats - very important to aquatic life
Density is used to characterize substances and to convert between volume and mass. For measuring out solids mass is generally more convenient, for measuring out liquids, volume is generally more convenient.
Sample Problem: What volume of isopropyl alcohol (rubbing alcohol) would you use if you needed 25g? Information: D = 0.7855 g / cm3 at 20oC
Does this make sense? Density less than one so the volume in mL (cm3) is greater than the mass in grams.
II. Specific gravity - often it is more convenient to measure the density of a substance relative to that of water
As it is a relative measure, it has no units, they divide out.
Where do we use hydrometers?
winemaking - monitoring the conversion of sugars to alcohol (ethanol) during fermentation
urine analysis - normal sg or uring 1.003 - 1.030. Abnormalities can indicate diabetes
diabetes mellitus (what many normally associate with the word diabetes) - high reading due to excess dissolved sugar (glucose) in the urine.
diabetes insipidus - low specific gravity, nearly colorless urine, very little dissolved material.
III. Heat capacity
Remember heat measured in Joules, calories (1 kcal = dietary Calorie)
1 cal = 4.18 J
Heat capacity (symbolized Cp, units: cal / oC, J / oC, etc... ) - quantity of heat required to change an objects temperature by 1oC. Depends on both the mass of an object (so it is an extrinsic property) and its composition.
The air contained in an over has a lower heat capacity than the metal racks. The metal racks can store more "heat" than the air. More energy as heat is transferred to your hand when you touch the rack than simply place your hand in the air of the oven.
Specific heat capacity (units: cal g-1 oC-1, J g-1 oC-1, etc... ) - not relative to something as with specific gravity.
quantity of heat required to raise the temperature of 1 gram of a substance 1oC. Takes into account weight so it is a property characterizing a material; it is an intrinsic property. Often better for making comparisons between materials.
The high specific heat of water means it can store a lot of energy (passive solar energy schemes - large drums of water)! Good at removing heat from other objects (sweat, nuclear reactors)
D = change
heat = m DT s.h.
where m is mass, DT is the change in temperature, and s.h. is the specific heat capacity
Problem: Taking a bath might use 95kg of water. How much energy (in cal and Joules) is needed to heat the water from 15oC to 40oC. Remember, specific heat of water is 1.0 cal / (g oC)
Change in temperature = DT = 40-15 = 25oC
Does it matter if we are in oC or K or oF?
mass = 95 kg = =95000 g = 9.5 x104 g
heat = (1.0 cal / (g oC))(25oC)(9.5x104g) = 2.375 x 106 cal
heat = (2.375 x 106 cal) (4.18 J / cal) = 9.927 x 105J = 9.9 x 105 J
A more compact approach: We can treat specific heat much like a conversion factor. Although unlike converting between pounds and kg, specific heat converts between three quantities (mass, heat, temperature change). If we know two, we can determine the third. As we can treat specific heat like a conversion factor, we can carry out the calculation much as we would carry out a unit convertion problem:
How much heat is this?
e.g. combustion (exothermic process) - ideally: carbon compound + oxygen -> carbon dioxide + water