This chapter is from the book
This chapter is from the book
This chapter is from the book
1.4 Units
Throughout this book we will use primarily the SI system of units with occasional use of the American Engineering system. The main quantities of interests are pressure, temperature, and energy. These are briefly reviewed below. Various physical constants that are commonly used in thermodynamics are shown in Table 1-1.
Table 1-1: Thermodynamic constants
Avogadro's number |
NA = 6.022 × 1023 mol−1 |
Boltzmann's constant |
kB = 1.38 × 10−23 J/K |
Ideal-gas constant |
R = kBNA = 8.314 J/mol K |
Absolute zero |
0 K = 0 R = −273.15 °C= −459.67 °F |
Pressure
Pressure is the ratio of the force acting normal to a surface, divided by the area of the surface. In thermodynamics, pressure generates the forces that give rise to mechanical work. The SI unit of pressure is the pascal, Pa, and is defined as the pressure generated by 1 N (newton) acting on a 1 m2 area:
)
The last equality in the far right is obtained by writing J = N · m. The pascal is an impractically small unit of pressure because 1 N is a small force and 1 m2 is a large area. A commonly used multiple of Pa is the bar:
)
An older unit of pressure, still in use, is the Torr, or mm Hg, representing the hydrostatic pressure exerted by a column of mercury 1 mm high. In the American Engineering system of units, pressure is measured in pounds of force per square inch, or psi. The relationship between the various units can be expressed through their relationship to the standard atmospheric pressure:
)
Temperature
Temperature is a fundamental property in thermodynamics. It is a measure of the kinetic energy of molecules and gives rise the sensation of “hot” and “cold.” It is measured using a thermometer, a device that obtains temperature indirectly by measuring some property that is a sensitive function of temperature, for example, the volume of mercury inside a capillary (mercury thermometer), the electric current between two different metallic wires (thermocouple), etc. In the SI system, the absolute temperature is a fundamental quantity (dimension) and its unit is the kelvin (K). In the American Engineering system, absolute temperature is measured in rankine (R), whose relationship to the kelvin is,
)
Temperatures measured in absolute units are always positive. The absolute zero is a special temperature that cannot be reached except in a limiting sense.
In practice, temperature is usually measured in empirical scales that were originally developed before the precise notion of temperature was clear. The two most widely used are the Celsius scale and the Fahrenheit. They are related to each other and to the absolute scales as follows:4
)
)
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where the subscript in T indicates the corresponding units. The units of absolute temperature are indicated without the degree (°) symbol, for example, K or R; the units in the Celsius and Fahrenheit scales include the degree (°) symbol, for example, °C, °F. Although temperatures are almost always measured in the empirical scales Celsius or Fahrenheit, it is the absolute temperature that must be used in all thermodynamics equations.
Mole (mol, gmol, lb-mol)
The mole5 is a defined unit in the SI system such that 1 mol is an amount of matter that contains exactly NA molecules, where NA = 6.022 × 1023 mol−1 is Avogadro’s number.6 The mass of 1 mol is the molar mass and is numerically equal to the molecular weight multiplied by 10−3kg. For example, the molar mass of water (molecular weight 18.015) is
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The symbol Mm will be used to indicate the molar mass. The number of moles n that correspond to mass m is
)
The pound-mol (lb-mol) is the analogous unit in the American Engineering system and represents an amount of matter equal to the molecular weight expressed in lbm. The relationship between the mol and lb-mol is
)
Energy
The SI unit of energy is the joule, defined as the work done by a force 1 N over a distance of 1 m, also equal to the kinetic energy of a mass 1 kg with velocity 1m/s:
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The kJ (1 kJ = 1000 J) is a commonly used multiple.
As a form of energy, heat does not require its own units. Nonetheless, units specific to heat remain in wide use today, even though they are redundant and require additional conversions when the calculation involves both heat and work. These units are the cal (calorie) and the Btu (British thermal unit) and are related to the joule through the following relationships:
)
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Some unit conversions encountered in thermodynamics are shown in Table 1-2.
Table 1-2: Common units and conversion factors
Magnitude |
Definition |
Units |
Other Units and Multiples |
Length |
- |
m |
1 cm = 10-2 m 1 ft = 0.3048 m 1 in = 2.54 × 10-2 m |
Mass |
- |
kg |
1 g = 10-3 kg 1 lb = 0.4536 kg |
Time |
- |
s |
1 min = 60 s 1 hr = 3600 s |
Volume |
(length)3 |
m3 |
1 cm3 = 10-6 m3 1 L = 10-3 m3 |
Force |
(mass)×(acceleration) |
N = kg m s-2 |
1 lbf = 4.4482 N |
Pressure |
(force)/(area) = (energy)/(volume) |
Pa = N m-2 |
1 Pa = 10-3 kJ/m3 1 bar = 105 Pa 1 psi = 0.06895 bar |
Energy |
(force)×(length) = (mass)×(velocity)2 |
J = kg m2 s-2 |
1 kJ = 103 J 1 Btu = 1.055 kJ |
Specific energy |
(energy)/(mass) |
J/kg |
1 kJ/kg=2.3237 kJ/kg 1 Btu/lbm=2.3237 kJ/kg |
Power |
(energy)/(time) |
W = J/s |
1 Btu/s = 1.055 kW 1 hp = 735.49 W |