Editing Joule–Thomson effect (section)

==Throttling in the ''T''-''s'' diagram==
[[File:Throttling in Ts diagram 01.jpg|450px|thumb|right|Fig. 2 – ''T''-''s'' diagram of nitrogen. The red dome represents the two-phase region with the low-entropy side (the saturated liquid) and the high-entropy side (the saturated gas). The black curves give the ''T''-''s'' relation along isobars. The pressures are indicated in bar. The blue curves are isenthalps (curves of constant specific enthalpy). The specific enthalpies are indicated in kJ/kg. The specific points a, b, etc., are treated in the main text.]]

A convenient way to get a quantitative understanding of the throttling process is by using diagrams such as ''h''-''T'' diagrams, ''h''-''P'' diagrams, and others. Commonly used are the so-called ''T''-''s'' diagrams. Figure 2 shows the ''T''-''s'' diagram of nitrogen as an example.<ref>Figure composed with data obtained with [[REFPROP]], NIST Standard Reference Database 23</ref> Various points are indicated as follows:{{ordered list
 | list-style-type=lower-alpha;
 | 1= ''T'' = 300{{nbsp}}K, ''p'' = 200 bar, ''s'' = 5.16{{nbsp}}kJ/(kgK), ''h'' = 430{{nbsp}}kJ/kg;
 | 2= ''T'' = 270{{nbsp}}K, ''p'' = 1 bar, ''s'' = 6.79{{nbsp}}kJ/(kgK), ''h'' = 430{{nbsp}}kJ/kg;
 | 3= ''T'' = 133{{nbsp}}K, ''p'' = 200 bar, ''s'' = 3.75{{nbsp}}kJ/(kgK), ''h'' = 150{{nbsp}}kJ/kg;
 | 4= ''T'' = 77.2{{nbsp}}K, ''p'' = 1 bar, ''s'' = 4.40{{nbsp}}kJ/(kgK), ''h'' = 150{{nbsp}}kJ/kg;
 | 5= ''T'' = 77.2{{nbsp}}K, ''p'' = 1 bar, ''s'' = 2.83{{nbsp}}kJ/(kgK), ''h'' = 28{{nbsp}}kJ/kg (saturated liquid at 1 bar);
 | 6= ''T'' = 77.2{{nbsp}}K, ''p'' = 1 bar, ''s'' = 5.41{{nbsp}}kJ/(kgK), ''h'' = 230{{nbsp}}kJ/kg (saturated gas at 1 bar).
}}

As shown before, throttling keeps ''h'' constant. E.g. throttling from 200 bar and 300{{nbsp}}K (point a in fig. 2) follows the isenthalpic (line of constant specific enthalpy) of 430{{nbsp}}kJ/kg. At 1 bar it results in point b which has a temperature of 270{{nbsp}}K. So throttling from 200 bar to 1 bar gives a cooling from room temperature to below the freezing point of water. Throttling from 200 bar and an initial temperature of 133{{nbsp}}K (point c in fig. 2) to 1 bar results in point d, which is in the two-phase region of nitrogen at a temperature of 77.2{{nbsp}}K. Since the enthalpy is an extensive parameter the enthalpy in d (''h''<sub>d</sub>) is equal to the enthalpy in e (''h''<sub>e</sub>) multiplied with the mass fraction of the liquid in d (''x''<sub>d</sub>) plus the enthalpy in f (''h''<sub>f</sub>) multiplied with the mass fraction of the gas in d (1 − ''x''<sub>d</sub>). So
:<math>h_d = x_d h_e + (1 - x_d) h_f.</math>

With numbers: 150 = ''x''<sub>d</sub> 28 + (1 − ''x''<sub>d</sub>) 230 so ''x''<sub>d</sub> is about 0.40. This means that the mass fraction of the liquid in the liquid–gas mixture leaving the throttling valve is 40%.