We measure time in many units, but the most common are years, months, weeks, days, hours, minutes, and seconds (table 4.6). A year is based on the time required for the earth to orbit the sun; so, it is also called a solar year. Slightly more than 365 days make up a year. In reality, it takes earth 365¼ days to make one orbit around the sun. Thus, a year is 365 days plus about 6 hours, or one-fourth of a 24-hour day. To keep calendars on track, every 4 years we add up the 6 hours and create an extra 24-hour day. We call this 366-day year a leap year. The 12 months making up a year have either 30 or 31 days, except for February, which has 28 days (excluding a leap year when it has 29). To keep track of how many days are in a particular month, remember the doggerel:
Thirty days hath September, April, June, and November.
All the rest have thirty-one, Save for February, Which has 28 alone.
Of course, you also have to remember that in a leap year, February has 29 days.
A day is 24 hours long. To keep track of time, conventional clocks are divided into two 12-hour periods—a.m. (midnight to noon) and p.m. (noon to midnight). The abbreviation a.m. is for the Latin ante meridiem, which means before noon. The abbreviation p.m. is for the Latin post meridiem, which means after noon. So, to state the correct time with conventional clocks, the time must be followed by a.m. or p.m.—for example, 10:07 a.m. or 4:10 p.m. As for the question: “Is 12 o’clock that follows 11:00 a.m., 12:00 a.m. or 12:00 p.m.?” the answer is that it is neither. Instead, it is 12 noon, just as 12 o’clock that follows 11:00 p.m. is 12 midnight.
To avoid confusion, the military has long used a 24-hour clock. Thus, they designate midnight as 0000, 1:00 a.m. as 0100 hours (spoken as oh-one-hundred hours), 2:00 a.m. as 0200, and so on. Noon is 1200 (spoken as twelve-hundred hours), 6 p.m. is 1800, and midnight is 2400 or 0000. Countries that use the metric system often use a 24-hour clock. In such cases, the time is written or spoken as, for example, 0935 (oh-nine-thirty-five) or 2115 (twenty-one-fifteen).
With a 24-hour clock a.m. and p.m. are not required.
TABLE 4.6 hours are added up and applied every 4 years to form leap year, which has 366 days.
We divide each hour into 60 minutes and 3,600 seconds. The second is the fundamental unit of time in the SI system. The standard second is the ephemeris second, an astronomical term having to do with the time it takes the earth to make one orbit around the sun. So, at one time, scientists defined a second in terms of the solar year, but, today, they define it in terms of the frequency of radiation from cesium atoms. Cesium is a soft, silvery white metal that is liquid at room temperature. Its radiation frequency is 9,192,631,770 hertz (cycles per second).
Because scientific equipment can measure this frequency accurately, scientists set clocks by it, which makes the clocks very accurate. Indeed, a cesium clock loses only 1 second of accuracy in 1 to 4 million years.
Seconds, minutes, hours, and days are the important units for describing the time rate at which something happens—for example, how many revolutions per minute (rpm) a motor makes as it rotates, how much fuel an aircraft consumes per hour of flight, and how many miles per hour a car travels.
Scientists measure very short intervals of time in milliseconds (ms or 10–3 s), microseconds (µs, or 10–6 s), and nanoseconds (ns, 10–9 s). A millisecond is one thousandth of a second, a microsecond is one millionth of a second, and a nanosecond is one billionth of a second.
Example Problem: An electric motor turns at 1,800 revolutions per minute (rpm).
How many revolutions does it make each second?
Solution: Perhaps the best way to solve this problem is to set up a proportional equation with x representing the unknown:
1,800 x –––– = 60 1
Another way of stating the problem is 1,800 is to 60 as x is to 1. Cross multiplying the figures results in:
60x = 1,800 × 1 60x = 1,800
x = 1,800 ÷ 60 x = 30.
The motor makes 30 revolutions per second.
Temperature and Measurement
The measurement and control of temperature are important aspects of everyday life and industry. Temperature, like pressure, forms a part of everyone’s environ-ment. Natural temperatures on the earth range from well below the freezing point of water to well above levels that we consider comfortable. Scientists and manufacturers often work with temperatures considerably higher and lower than normal. Theoretically, the lowest temperature is absolute zero, which is defined as the temperature at which molecular movement in a substance ceases. Up to now, laboratories have not been able to achieve absolute zero; however, they have come to within a fraction of a degree.
The conventional measurement system expresses temperature in degrees Fahrenheit (°F). Daniel Gabriel Fahrenheit, a German physicist working in the Netherlands, invented the Fahrenheit scale of temperature measurement in the early 1700s. Important points on the Fahrenheit scale are the temperature of water at its freezing point (32°F) and its boiling point (212°F).
Time and Temperature 97
98 SOME PHYSICAL QUANTITIES AND THEIR MEASUREMENT
Most of the world measures temperature in degrees Celsius (°C).
This scale is named after its inventor, Anders Celsius, who was a Swedish mathematician and astronomer in the mid-1700s. In the days before SI, the original metric system used an identical scale: the centigrade scale. When the SI system was introduced, the measurement specialists needed a new name for the centigrade scale. The word centigrade contains an important prefix (centi) and using it would introduce an awkward anomaly into the system.
The solution was to honor the inventor of the scale, Anders Celsius. On the Celsius scale, 0° is the temperature at which water freezes and 100° is the temperature at which water boils.
The kelvin scale is the absolute temperature scale for metric measurements.
The temperature of –273.16 kelvin (K) corresponds to 0°C. The degree sign (°) is not used with kelvin, and the term kelvin is not written with an uppercase K, although an uppercase K is the symbol for degrees kelvin. Its inventor was William Thompson, who was also Lord Kelvin. Kelvin was a physicist born in Northern Ireland and devised his scale in 1848.
Another absolute temperature scale is degrees Rankine (°R). Based on the Fahrenheit scale, it serves the conventional system of measurements. It was named after William R.M. Rankine, a Scottish engineer who set it up in the mid-1800s.
The Fahrenheit and Celsius scales are in common use for everyday func-tions such as weather forecasting, heating, cooling, cooking, and medical care.
The absolute scales are mainly used in scientific applications. For example, the various laws relating to behavior of gases require the use of absolute scales.
Figure 4.8 shows the relationship of the four temperature scales. Table 4.7 shows how these scales are related through equations.
212° 672° 100° 373
32° 492° 0° 273
0° 460°
40° 420° -40° 233
-460° F 0° R -273° C 0 K
KELVIN CELSIUS
RANKINE FAHRENHEIT
STEAM POINT (WATER BOILS)
ICE POINT (WATER FREEZES)
ABSOLUTE ZERO FAHRENHEIT AND CELSIUS EQUAL AT -40°
Figure 4.8 A comparison of various temperature scales
TABLE 4.7 Temperature Scales
Scale Equivalents
°F 9⁄5°C + 32, or 1.8°C + 32
9⁄5(K – 273) + 32, or 1.8(K – 273) + 32
°R – 460
°C 5⁄9(°F – 32), or (°F – 32) ÷ 1.8
K – 273
5⁄9(°R – 492), or (°R – 492) ÷ 1.8
°R °F + 460
9⁄5K, or 1.8K
9⁄5°C + 492, or 1.8°C + 492
K °C + 273
5⁄9°R, or °R ÷ 1.8
5⁄9(°F – 32) + 273, or (°F + 460) ÷ 1.8
Time and Temperature 99
Example Problem: Convert 250°F to Celsius.
Solution: Use the formula for converting Celsius to Fahrenheit.
°C = 5⁄9(°F – 32°) = 5⁄9(250°F – 32°) = 5⁄9(218)
= (5 × 218) ÷ 9 = 1,090 ÷ 9
°C = 121.11 or
°C = (°F – 32°) ÷ 1.8 = (250°F – 32°) = 218 ÷ 1.8
°C = 121.11.
Example Problem: Convert –2.5°C to Fahrenheit.
Solution: Use the formula for converting Fahrenheit to Celsius.
°F = 9⁄5°C + 32
= (9 × –2.5) ÷ 5 + 32 = (–22.5 ÷ 5) + 32 = –4.5 + 32
°F = 27.5 or
°F = 1.8°C + 32 = (1.8 × –2.5) +32 = –4.5 + 32
°F = 27.5
100 SOME PHYSICAL QUANTITIES AND THEIR MEASUREMENT
Practice Problems
Refer to tables 4.6 and 4.7 to solve these problems.
1. An airliner traveled 3,975 miles from Dallas, Texas to Honolulu, Hawaii in 7½ hours.
a. What was its average speed in miles per hour?
_____________________________________________________
b. What was its speed in miles per minute?
_____________________________________________________
2. The capacity of a pump is 1,000 gallons per minute. How long will it take to fill a 500-barrel tank? (42 gal = 1 bbl)
_________________________________________________________
3. For every 90 revolutions of a pumping engine, the pump rods are raised and lowered once. If there are 15 strokes per minute, what is the rpm of the engine?
_________________________________________________________
4. Convert the following temperatures to Fahrenheit:
a. 345 K ________________________________________________
b. 20°C _________________________________________________
c. 0°C __________________________________________________
d. 482°R ________________________________________________
e. –78°C ________________________________________________
5. Convert the following temperatures to Celsius:
a. –89°F ________________________________________________
b. 32°F _________________________________________________
c. 277 K ________________________________________________
d. 432°R ________________________________________________
e. 10 K _________________________________________________
6. What are the Celsius temperature values for the following Kelvin values?
a. 324 K ________________________________________________
b. 203 K ________________________________________________
c. 293 K ________________________________________________
d. 250 K ________________________________________________
e. 49 K _________________________________________________
7. What are the conventional absolute temperature values for the following Fahrenheit temperatures?
a. 680°F ________________________________________________
b. 3°F __________________________________________________
c. 43°F _________________________________________________
d. –24°F ________________________________________________
e. –113°F _______________________________________________
8. In batching products through a pipeline, the rate of travel of the fluid through a 50-mile pipeline is 1.8 miles per hour. A new batch is started at 9:00 a.m.
on a Tuesday. When will the batch first arrive at the terminal end?
___________________________________________________________
9. At a loading dock for oil tankers, oil is delivered to a tanker at the rate of 10,000 barrels per hour. How many minutes will it take to load a 16,500-bar-rel tanker?
___________________________________________________________
10. Convert 325 degrees Rankine to the metric absolute temperature equivalent.
___________________________________________________________