Engineering Units, Part 1
Whether you are designing, specifying or operating a process, you will need an instinct for the nature and size of engineering units. In this two-part series, I'll look at some of the units in common use and help you get a feel for how big they are, how you can best manipulate them and how to minimize the problems of mixing them.
A web search for "engineering units" shows conversion programs and utilities dominating the returns. One offer claims it "supports over 400,000 conversions." It is no surprise that the obstacle course of different units can impede -- even endanger -- your day-to-day work.
You probably don't need reminding of the 23 mile glide and safe crash landing of a Boeing 767 in Gimli, MB, out of fuel because of a miscalculation between liters and fuel weight, or of the $125 million Mars Climate Orbiter, lost owing to confusion between metric and nonmetric units. These two real-life examples only help to underscore how important it is to use engineering units effectively.
TemperatureKelvin. The Kelvin scale goes from absolute zero (0K or zero Kelvins), through 273.15K (called the ice point), through 373.15K (called the steam point), where water begins to boil at normal atmospheric pressure. I hesitate to say where it ends. The unit K is called the Kelvin -- not the degree Kelvin -- and is the same size as the Celsius degree. Temperature difference also is given in Kelvins rather than oC.
Celsius. The Celsius scale takes its zero (0oC) at the ice point and 100oC at the steam point. It follows the Kelvin scale but has a 273.15K downward offset.
Fahrenheit. The Fahrenheit scale is derived from Tf = 9/5 Tc+32. This puts the ice point at 32oF and the steam point at 212oF.
A few examples of how different temperatures look or feel are shown in table 1.
Force, Energy and PowerIf you accelerate mass of one kilogram at 1 m/sec/sec, you will need a force of one newton. The gravitational force on a 102 g apple (a bit less than 1/4 lb) is about one newton. Think of Isaac Newton.
If you exert a force of one newton through a distance of 1 m, you will expend energy equal to one joule, or 1 J.
If you maintain this at a rate of 1 J/sec, your power level is one watt, or 1 W. So, 1 W maintained for 1 sec delivers 1 J. Note that energy is the same stuff whether it is mechanical, electrical, thermal or chemical, so you can use the same units.
Specific HeatSpecific heat is the energy required to raise the temperature of one gram of a substance by 1oC. It is commonly expressed in gram calories, and the value for water is one. All other substances have values less than one.
When expressed in joules per gram per degree Celsius (J/g-oC), the value is 4.18 times the gram calorie value.
Specific heat is somewhat dependent on temperature, but this usually can be ignored for small temperature ranges. The kilogram calorie (the one used by Weight Watchers) is, of course, 1,000 times the size of the gram calorie.
How Much Energy Do You Need?Now I will take a look at how much energy you need to heat water, air and a continuous airstream.
To Heat Water. Figure 1 shows a power source applied to 1 g of ice, starting at -10oC and maintained long enough to turn all the ice to water vapor.
Stage A. Ice is heated up from -10 to 0oC. The specific heat of ice around this temperature is about 2.09 J/g oC. Energy input equals mass times specific heat times temperature rise, or 1 x 2.09 x 10 = 20.9 J. The ice has not yet started to melt.
Stage B. The ice/water mixture remains at 0oC -- even though heat is being added -- until all of the ice melts. Given that the latent heat of fusion of water is 333 J/g, the heat required to melt the ice is mass times latent heat of fusion, or 1 x 333 = 333 J.
Stage C. The rise from 0 to 100oC does not involve a phase change to the water, and all the applied heat -- 419 J -- is used in raising the temperature. Specific heat of water is about 4.19 over this range.
Stage D. Another phase change occurs as the 1 g of water at 100oC changes to 1 g of steam at 100oC. Given that 2,260 J/g is the heat of vaporization for water, this takes 2,260 J.
Stage E. Heat is being added with no phase change occurring. Using a specific heat of 2.01 J/g oC, it takes 2.01 J for every oC that the steam temperature increases around this point on the graph.
The high specific heat and heat of vaporization of water make it an excellent medium for process cooling or dumping waste heat.
Next month, I'll show how the joule and gram are used in the workplace.