Modern Engineering Thermodynamics

6.6 Throttling Devices 181
For an ideal gas with constant specific heats, we can substitute Eq. (6.22) into Eq. (6.23) to obtain
T out = T in + ðV 2 in − V2 out Þ/ð2g cc p Þ
This equation tells us that, in the case of negligible change in specific kinetic energy, the throttling of an ideal
gas is an isothermal process.
The actual throttling device outlet temperature for a pure substance is dependent on its Joule-Thomson coefficient
μ J , defined as
μ J = ð∂T/∂pÞ h
(6.25)
Since μ J is defined completely in terms of intensive thermodynamic properties, it too is an intensive thermodynamic
property. A throttling process that has a negligible change in specific kinetic energy is a process of constant
h, so the Joule-Thomson coefficient for any pure substance can be approximated from data taken during
such a throttling process as
μ J ≈ ðΔT/ΔpÞ throttling
process
(6.26)
If we take Δp = p out − p in , then Δp normally is a negative number for such a process. Clearly, a positive value for
μ J means that the temperature drops during such a throttling process (ΔT = T out − T in < 0) and a negative value
for μ J means that the temperature increases. For an isothermal throttling process (such as occurs with an ideal
gas), μ J =0.
A gaseous pure substance that has a positive Joule-Thomson coefficient could undergo a continuous decrease
in temperature and eventually be liquified by a properly designed throttling process. This was the basis of
a process introduced in 1895 by Karl von Linde (1842–1934) for the large-scale production of liquid air.
The temperature at which μ J = 0 for a real pure substance is called its inversion temperature T inv ,andμ J > 0for
T < T inv and μ J < 0forT > T inv . Thus, the temperature of a real gas decreases in a throttling process if its
inlet temperature is less than its inversion temperature. However, the temperature of a gas cannot be lowered
via the Joule-Thomson effect if the gas inlet temperature exceeds its “maximum” inversion temperature
(see Table 6.3). 6
Figure 6.6 shows the variation in the Joule-Thomson coefficient with pressure and temperature for air and
carbon dioxide.
Table 6.3 The Maximum Joule-Thomson Inversion Temperature for Various Common Gases
Substance
K
Maximum Inversion Temperature
Air 659 1186
Argon 780 1404
Carbon dioxide 1500 2700
Helium 40 72
Hydrogen 202 364
Neon 231 416
Nitrogen 621 1118
Oxygen 764 1375
Source: Reprinted by permission of the publisher from Zemansky, M. W., Abbott, M. M., Van Ness, H. C., 1975. Basic Engineering
Thermodynamics, second ed. McGraw-Hill, New York.
R
6 Since the condition μ J = 0 can occur at more than one temperature, a gas may have several inversion temperatures, the largest of
which is its “maximum” inversion temperature.