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23 August 2012 - 13:09Units

Powers of ten

Check this out to get some sense of how orders of magnitude impact our understanding of scale in length (but the same idea applies to mass, energy, etc).

Check out wikipedia if you’re not feeling awesome about SI units.


Typically engineers work in the range of microns (10-6 m) to kilometers (103 m). Some engineers (e.g., biomedical engineers) think more about nanoscale problems outside this range on the low end while other engineers (e.g., civil engineers) think about problems on scales of thousands of kilometers.  See the link above in powers of ten to think a little bit outside this range of scales.


Mass in green engineering problems is typically expressed in the SI units of kilograms though oftentimes we are looking at really big problems. For example, to know how much mass there is in all the roadways in America or how much carbon we emit into the atmosphere each year. For these problems we often will use short tons (2000 lbs) or metric tonnes (1000 kg). Large quantities (like carbon emissions) are expressed in terms of gigatons (1000000000000 or 109 kg)


The SI unit for power is the Watt:

\mathrm{W = \frac{J}{s} = \frac{N\cdot m}{s} = \frac{kg\cdot m^2}{s^3}}

An average sized coal fired power plant produces about 500-700 MW of electricity.


The SI derived unit for energy is the Joule, which is:

\rm J  = {}\rm \frac{kg \cdot m^2}{s^2} = N \cdot m = \rm Pa \cdot m^3={}\rm W \cdot s

A barrel of oil has about 6 GJ of energy.


In water

Water pollution units are simpler than air pollution units. Water pollution is typically expressed either in terms of weight per volume (e.g., mg/L or μg/L) or in the dimensionless form of the weight of contaminant per weight of water solution (mg/kg → ppmw or μg/kg → or ppbw). We can convert between the two units by using the density of water ρw = 1 kg/L to convert volume of water to weight of water. Once in fractional form with common weight unit (e.g., g/g), multiply by 106 or 109 to get ppmw or ppbw.

In air

Air pollution units are typically expressed as parts per million (volume). We can understand this by thinking back to the ideal gas law, where P: pressure (Pa; 1 atm = ~1.01 x 105 Pa), T: temperature (ºK = ºC + 273.15), R: gas constant (8.314 J-mol-1K-1=8.21×10-5 atm-m3-mol-1K-1), n: number of moles, and V: volume. Recall also the definition of partial pressure or partial volume or partial molar volume, where for some mixture, the total pressure or volume is the sum of the pressure or volume of all the constituents in the mixture. We recognize that for all gases, the ratio of P, V, and n in mixtures is constant. We can rewrite the ideal gas equation in terms of either partial pressure or partial volume (things we can easily measure).


The definition of part per million volume is 106 Vi/V

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