, typically
symbolized by the Greek letter rho (
). Density has both a value and units.
There are a number of definitions and tools used to specify the amounts of material entering and leaving processes.
Density is the mass per unit volume of a substance , typically
symbolized by the Greek letter rho (). Density has both a value and units.
Density is used to relate mass and volume of a substance.
Gas/vapor densities depend heavily on Pressure and Temperature. You must almost always treat them as direct functions of P, T, or both. You usually will need to calculate a gas density value; liquid and solid values can normally be looked up in a table.
Densities
of pure solids and liquids also vary when pressure and temperature change, but
much less.
Because they don't change much, solid and liquid densities are often treated as constants. This is an example of an engineering "assumption" -- we will frequently "assume constant density" for a solid or liquid as we set up a problem in order to make it easier to solve. It is important that we always list our assumptions, so that they can be quickly reviewed if the problem solution seems inadequate or if problem conditions change.
We may also assume specific values if circumstances warrant. For instance, in most applications we'll assume the density of water to be 1.0 gram per cubic centimeter, even though that is strictly true only for a specific temperature range.
The specific volume of a substance is the volume per unit mass, the reciprocal of the density.
The specific gravity is the ratio of the density of a substance to that of a reference substance.
Usually the reference substance for solids and liquids is water at 4 degrees Celsius.
For gases, the usual reference density is that of air.
The petroleum industry has traditionally used 60 degrees Fahrenheit as the reference point. This won't matter much in this class, but you need to be careful if you consult reference works.
Since density varies with temperature, many workers like the added precision of specifying the temperatures involved. They might write a specific gravity value as:
We generally want to know how much material is coming into or out of a process, so we measure the "flow rate":
Usually, the volumetric flow rate is the easiest to measure. It can then be converted to mass flow rate using the density:
Most industrial flow measurement devices really measure the flow velocity. The volumetric flow rate is then calculated from the velocity and the cross-sectional area of the pipe:
A Mole is a measure of quantity of substance or the number of particles. A gram-mole (mol, gmol) of a species is the amount of a species whose mass in grams is numerically the same as its molecular weight.
Carbon Dioxide has a molecular weight of 44, so 1 mol of CO2 contains 44 grams.Hint: If the molecular weight of a substance is M, then there are M grams per gram-mole. This means you can use the molecular weight as a conversion factor for going from mass to moles.
To simplify engineering problems, we will also use kilogram-moles (kgmol) and pound-moles (lbmol, mole). These are defined the same way but using different mass units.
1 lbmol of CO2 contains 44 lbs (or 19,976 grams -- a lot more than a gmol!)
You use the same conversion factors for the different flavors of mole as you do for converting mass units (454 g-mole = 1 lbmole, etc.).
The molecular weight is used to convert from mass to moles, so it is logical that it is also used to convert between mass and molar rates:
References:
R.M. Price
Original: 6/2/94
Modified: 8/24/95, 8/13/96, 8/25/98; 5/24/2004
Copyright 2004 by R.M. Price -- All Rights Reserved
