Modern Engineering Thermodynamics

2.7 Pressure and Temperature Scales 41
WHO DEVELOPED THE IDEAL GAS EQUATION OF STATE?
By 1662, the English chemist Robert Boyle (1627–1691) had conducted experiments establishing that the pressure of a gas
varies inversely with the volume when the temperature is held constant. In the early 1800s, the French physicists Jacques
Charles (1746–1823) and Joseph Gay-Lussac (1778–1850) independently determined that the volume V of a gas increases
linearly with temperature when the pressure is held constant. The Charles/Gay-Lussac relation can be written as
V
= 1 + αT
V 0
where T is in °C and V 0
is the volume of the gas at 0°C. The empirical constant α is the coefficient of thermal expansion of
the gas and was found to have the same value for all gases as the pressure approached zero.
α = 0:003661°C − 1 1
=
273:15 °C − 1
Since α is the same for all gases at low pressure, the Charles/Gay-Lussac equation provides a single calibration point (at V 0
)
temperature scale that is independent of the type of gas used, plus it defines the “size” of the degree (αV 0
) on the scale.
By 1820, the Boyle and Charles/Gay-Lussac results had been combined to produce the “ideal” gas equation of state:
h
pV = mR Tðin °CÞ + 1 i
= mR½Tðin °CÞ + 273:15Š
α
and by then it was generally accepted that T (in °C) + 273.15 corresponded to some sort of ideal gas absolute temperature
scale. However, the problem remained that this scale still appeared to depend on the thermometric measuring material (an
ideal gas) and therefore did not constitute a genuine “thermodynamic” absolute temperature scale.
Since the concept of an absolute temperature scale was not firmly established until 1848 by Lord Kelvin, it is remarkable
that the ideal gas equation of state, which depends on the use of an absolute temperature scale, was in use a full 30 years
earlier. However, historically, we find that empirical equations often precede theoretical explanations.
HOW IS GAUGE PRESSURE RELATED TO ABSOLUTE PRESSURE?
Absolute pressure = Gauge pressure + Local atmospheric pressure
HOW DO I KNOW IF A GIVEN SI PRESSURE IS ABSOLUTE OR GAUGE?
When an SI pressure appears in a textbook without such an identifier (e.g., 3.75 MPa), assume that it is an absolute
pressure (i.e., 3.75 MPa-absolute). Gauge pressures should always be identified as “gauge” to avoid confusion.
Temperature level
Pressure
level 2
Freezing point
of water
Relative
temperature
Absolute
temperature
Atmospheric
pressure
Pressure
level 1
Gauge
pressure 2
Vacuum 1
Absolute
pressure 2
Absolute
pressure 1
Absolute
zero temperature
Absolute
zero pressure
(a) Temperature
(b) Pressure
FIGURE 2.5
Relative and absolute temperatures and pressures.