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CHAPTER12

# Plotting the temperatures against the pressures gives

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Unformatted text preview: look at its defining equation reveals that the Joule-Thomson coefficient represents the slope of h constant lines on a T-P diagram. Such diagrams can be easily constructed from temperature and pressure measurements alone during throttling processes. A fluid at a fixed temperature and pressure T1 and P1 (thus fixed enthalpy) is forced to flow through a porous plug, and its temperature and pressure downstream (T2 and P2) are measured. The experiment is repeated for different sizes of porous plugs, each giving a different set of T2 and P2. Plotting the temperatures against the pressures gives us an h constant line on a T-P diagram, as shown in Fig. 12–13. Repeating the experiment for different sets of inlet pressure and temperature and plotting the results, we can construct a T-P diagram for a substance with several h constant lines, as shown in Fig. 12–14. Some constant-enthalpy lines on the T-P diagram pass through a point of zero slope or zero Joule-Thomson coefficient. The line that passes through these points is called the inversion line, and the temperature at a point where a constant-enthalpy line intersects the inversion line is called the inversion temperature. The temperature at the intersection of the P 0 line (ordinate) and the upper part of the inversion line is called the maximum inversion temperature. Notice that the slopes of the h constant 0) at states to the right of the inversion line and lines are negative (mJT positive (mJT 0) to the left of the inversion line. A throttling process proceeds along a constant-enthalpy line in the direction of decreasing pressure, that is, from right to left. Therefore, the temperature of a fluid increases during a throttling process that takes place on the right-hand side of the inversion line. However, the fluid temperature decreases during a throttling process that takes place on the left-hand side of the inversion line. It is clear from this diagram that a cooling effect cannot be achieved by throttling unless the fluid is below its maximum inversion cen84959_ch12.qxd 4/5/05 3:58 PM Page 669 Chapter 12 temperature. This presents a problem for substances whose maximum inversion temperature is well below room temperature. For hydrogen, for example, the maximum inversion temperature is 68°C. Thus hydrogen must be cooled below this temperature if any further cooling is to be achieved by throttling. Next we would like to develop a general relation for the Joule-Thomson coefficient in terms of the specific heats, pressure, specific volume, and temperature. This is easily accomplished by modifying the generalized relation for enthalpy change (Eq. 12–35) dh cp dT cv Ta 0v b d dP 0T P | 669 For an h constant process we have dh rearranged to give 1 cv cp Ta 0v bd 0T P a 0. Then this equation can be 0T b 0P h m JT (12–52) which is the desired relation. Thus, the Joule-Thomson coefficient can be determined from a knowledge of the constant-pressure specific heat and the P-v-T behavior of the substance. Of course, it...
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