Modern Engineering Thermodynamics

40 CHAPTER 2: Thermodynamic Concepts
2.7 PRESSURE AND TEMPERATURE SCALES
Because of the historical manner in which the concepts of pressure and temperature evolved, we are forced to
deal with two scales for each. We have a relative and an absolute scale for both temperature and pressure
measurement. Some formulae allow the use of either scale in calculations, but other formulae require the use of
only absolute scales in calculations. Therefore, it is very important to know which scales are being used when
you are given values for temperature and pressure.
As we saw in Chapter 1, there are two common absolute temperature scales, Rankine (R) and Kelvin (K). They
are related as follows: 4 TðRÞ = 9 TðKÞ (2.1)
5
Each of these absolute scales has a relative scale, the common English Fahrenheit (°F)scaleandtheEuropean
Celsius (°C) scale. 5 These two relative scales are related to each other by
and the respective absolute and relative scales are related by
Tð°FÞ = 9 T ð°CÞ + 32 (2.2)
5
TðRÞ = Tð°FÞ + 459:67 (2.3)
and
TðKÞ = Tð°CÞ + 273:15 (2.4)
Pressure can be viewed as a compressive stress. Thus, absolute zero pressure corresponds to a level of zero stress.
However, even though we generally do not encounter negative absolute pressures in thermodynamics, any finite
tensile stress in a fluid or a solid is equivalent to its being subjected to a negative absolute pressure. There is no
lack of consistency here; this is merely a standard sign convention for stress.
Because most gauges manufactured to measure pressure were designed to read zero at local atmospheric
pressure, their readings constitute a relative pressure scale, called gauge pressure.
To distinguish between gauge and absolute pressure values in our writing, we append the letter g or a to the
English units of the term. Therefore, the English pressure units psia and psig are to be read “pounds per square
inch absolute” and “pounds per square inch gauge,” respectively. SI pressure units should carry the identifying
words absolute or gauge (e.g., 3.75 MPa-absolute or 3.75 MPa-gauge). This is a clumsy indicator, and since
thermodynamic tables are always given in absolute pressure units and thermodynamic equations work with
absolute pressure units, SI pressures are generally assumed to be in absolute units even when not so specified.
Unless otherwise specified in a problem statement, the local atmospheric pressure should always be taken to be
the standard atmospheric pressure, which is 14.696 psia (or 14.7 psia) or 101,325 Pa (or 101.3 kPa). Figure 2.5
illustrates the meanings of relative and absolute temperature and pressure.
If you are given a formula with a quantity such as p or T in it, how do you know which scale to use?
The following boxed rule of thumb titled “How Do I Know When I Have to Use Absolute Pressure or Temperature?”
provides the answer.
In the ideal gas equation of state,
pV = mRT (2.5)
both the quantities p and T stand alone, so that the values substituted for them must always be in an absolute
scale (psia and R or Pa-absolute and K). On the other hand, if a formula contains the difference in a quantity not
raised to a power, such as p 2 – p 1 (or Δp), or T 2 – T 1 (or ΔT), then the values assigned to that quantity may be in
either absolute or relative scale units. For example, if we have an ideal gas in a closed system of constant volume
V, then when the gas is in state 1, we can write
p 1 V = mRT 1 (2.6)
4 Recall from Chapter 1 that, since 1967, we no longer use the degree prefix on the absolute temperature scales but retain it on the
relative scales. Hence, we write 100 R for a temperature of 100 rankine, not 100°R.
5 The Celsius scale was also commonly called the centigrade scale. However, the centigrade—from the Latin for 100 (centi) divisions
(grade)—scale was developed by the Swedish astronomer Anders Celsius in about 1742; and in 1948, the centigrade scale was officially
renamed the Celsius scale.