Physical Chemistry , 1st ed.

For an ideal gas,JTis exactly zero, since enthalpy depends only on tempera-

ture (that is, at constant enthalpy, temperature is also constant). However, for

real gases, the Joule-Thomson coefficient is not zero, and the gas will change

temperature for the isenthalpic process. Remembering from the cyclic rule of

partial derivatives that



T

p



H



H

T



p



H

p



T

 1

we can rewrite this as



T

p



H



and, recognizing that the left side is JTand the denominator of the fraction

is simply the heat capacity at constant pressure, we have

JT (2.35)

This equation verifies that JTis zero for an ideal gas, since ( H/ p)Tis zero

for an ideal gas. Not for realgases, however. Further, if we measure JTfor real

gases and also know their heat capacities, we can use equation 2.35 to calcu-

late ( H/ p)Tfor a real gas, which is a quantity (the change in enthalpy as pres-

sure changes but at constant temperature) that is difficult or impossible to

measure by direct experiment.

Example 2.11

If the Joule-Thomson coefficient for carbon dioxide, CO 2 , is 0.6375 K/atm,

estimate the final temperature of carbon dioxide at 20 atm and 100°C that is

forced through a barrier to a final pressure of 1 atm.

Solution

Using the approximate form of the Joule-Thomson coefficient:

JT (^) 





T

p



H

pin this process is 19 atm (the negative sign meaning that the pressure is

going downby 19 atm). Therefore, we have

 1



9

T

atm



H

0.6375 K/atm

Multiplying through:

T12 K

which means that the temperature drops from 100°C to about 88°C.

The Joule-Thomson coefficient of real gases varies with temperature and

pressure. Table 2.2 lists some experimentally determined JTvalues. Under

some conditions, the Joule-Thomson coefficient is negative, meaning that as



H

p



T



Cp



H

p



T





H

T



p

44 CHAPTER 2 The First Law of Thermodynamics