Thermodynamics

668 | Thermodynamics>T 1 = 20°C T 2 = 20°C 0 µ JT < 0Maximum inversiontemperatureh = const.Inversion lineFIGURE 12–14Constant-enthalpy lines of a substanceon a T-P diagram.PP12–5 ■ THE JOULE-THOMSON COEFFICIENTWhen a fluid passes through a restriction such as a porous plug, a capillarytube, or an ordinary valve, its pressure decreases. As we have shown inChap. 5, the enthalpy of the fluid remains approximately constant duringsuch a throttling process. You will remember that a fluid may experience alarge drop in its temperature as a result of throttling, which forms the basisof operation for refrigerators and air conditioners. This is not always thecase, however. The temperature of the fluid may remain unchanged, or itmay even increase during a throttling process (Fig. 12–12).The temperature behavior of a fluid during a throttling (h constant)process is described by the Joule-Thomson coefficient, defined as(12–51)Thus the Joule-Thomson coefficient is a measure of the change in temperaturewith pressure during a constant-enthalpy process. Notice that ifm JT •m a 0T0P b h6 0 temperature increases 0 temperature remains constant7 0 temperature decreasesduring a throttling process.A careful look at its defining equation reveals that the Joule-Thomsoncoefficient represents the slope of h constant lines on a T-P diagram.Such diagrams can be easily constructed from temperature and pressuremeasurements alone during throttling processes. A fluid at a fixed temperatureand pressure T 1 and P 1 (thus fixed enthalpy) is forced to flow through aporous plug, and its temperature and pressure downstream (T 2 and P 2 ) aremeasured. The experiment is repeated for different sizes of porous plugs,each giving a different set of T 2 and P 2 . Plotting the temperatures againstthe pressures gives us an h constant line on a T-P diagram, as shown inFig. 12–13. Repeating the experiment for different sets of inlet pressure andtemperature and plotting the results, we can construct a T-P diagram for asubstance with several h constant lines, as shown in Fig. 12–14.Some constant-enthalpy lines on the T-P diagram pass through a point ofzero slope or zero Joule-Thomson coefficient. The line that passes throughthese points is called the inversion line, and the temperature at a pointwhere a constant-enthalpy line intersects the inversion line is called theinversion temperature. The temperature at the intersection of the P 0line (ordinate) and the upper part of the inversion line is called the maximuminversion temperature. Notice that the slopes of the h constantlines are negative (m JT 0) at states to the right of the inversion line andpositive (m JT 0) to the left of the inversion line.A throttling process proceeds along a constant-enthalpy line in the directionof decreasing pressure, that is, from right to left. Therefore, the temperatureof a fluid increases during a throttling process that takes place on theright-hand side of the inversion line. However, the fluid temperaturedecreases during a throttling process that takes place on the left-hand side ofthe inversion line. It is clear from this diagram that a cooling effect cannotbe achieved by throttling unless the fluid is below its maximum inversion