Table: Gas Constant for
Universal Gas Constant Versus
The relationship between pressure and temperature for most gases
can be approximated by the ideal gas law,
where p is the absolute
pressure, V is the
volume, m is the mass, T is the absolute temperature (units in Kelvin
or Rankine) and R is the gas constant. Kelvin is related to Celsius by
TK = TC + 273.15 and Rankine is related to Fahrenheit
byTR = TF + 459.67.
equation is also referred to as the perfect gas law or the equation of
an ideal gas. The gas constant R for some common gases is given in the
table. Note that the density ρ is given by m/V,
hence the ideal gas law can be written in terms of the density as
p = ρRT
The ideal gas law can also be written in per mole basis as follows:
where n is the number of moles and is
the universal gas constant. The number of moles is given by n = m/M where M is
the molecular weight of the
gas. The universal gas constant is
8.314 kJ/kmol-K for all gases, and it is related to the gas constant by:
Table: Critical Pressure and
Compressibility Chart for
Temperature for Various Gases*
Validity of the Ideal Gas Law**
Having introduced the ideal gas law, the
next important question is: Under what conditions will the ideal gas
law be a good approximation
for real gases? To address this issue, the compressibility factor
Z is introduced, and it is defined as:
Z = pV/mRT
Obviously, when Z approaches unity, then the ideal gas law holds.
factor for various gases is plotted as a function of the reduced pressure
(pR) and reduced temperature (TR) in the compressibility
chart as shown in the figure. The reduced pressure and temperature are
defined as follows:
pR = p/pc
TR = T/Tc
where pc and Tc are the critical pressure and
critical temperature, respectively. The critical temperature is the maximum
temperature that liquid and vapor phases can coexist in equilibrium.
pressure is the critical pressure. Values of critical pressure and temperature
for some common gases are summarized in the table.
From the compressibility chart, it is observed that Z approaches unity
when pR < 0.1 or TR > 2. Hence, these are
the conditions when the behavior of real gases can best be approximated
using the ideal gas law.
* Source: Sonntag, R. E. and Borgnakke, C., "Introduction
to Engineering Thermodynamics," John Wiley, Inc., New York,
** Reference: Su, G. J., "Modified Law
of Corresponding States," Ind. Eng. Chem. (international ed.), Vol.
38, pp. 803, 1946.