Cooling at constant pressure

If a one-component system is allowed to cool at constant pressure, and the temperature is recorded as a function of time, it looks as shown in Fig. A1.9. It shows five regions ... 

For points 2-3, there is constant entropy (S) compression for a one pound of air from Pg to P3. From points 3-5 the air cools at constant pressure, and gives up heat, Q, to the intercooler. From points 5-6 the air is compressed at constant S to the final pressure Pg. Note that point Tj = point Tg for constant temperature. For minimum work Tg = T3. Then the heat, Q, equals the Work, Wl of Figure 12-36B. Figure 12-38 is convenient for estimating the moisture condensed from an airstream, as well as establishing the remaining water vapor in the gas-air. 

J. A. C. Charles (1746-1823) observed, and J. L. Gay-Lussac (1778-1850) confirmed, that when a given mass of gas is cooled at constant pressure, it shrinks by times its volume at 0°C for every degree Celsius that it is cooled. Conversely, when the mass of gas is heated at constant pressure, it expands by times its volume at 0°C for every degree Celsius that it is heated. The changes in volume with temperature of two different-sized samples of a gas are shown in Fig. 11-6. 

Let us first consider how the density of the condensed phase changes with temperature. As our material in the vapour phase is cooled at constant pressure the density increases until the boiling point is reached. Further cooling then allows us to differentiate between the vapour and liquid states by the formation of a boundary. Further cooling increases the liquid density but at a much slower rate than that of the gaseous phase. The density of many liquids can be described by a simple linear equation over a wide temperature range 5... 

DEW POINT. The temperature to which a given parcel of air must be cooled at constant pressure and constant watervapnr content in order for saturation to occur, ihc temperature at which the saturation vapor pressure of the parcel is equal tu the actual vapor pressure of ihc contained water vapor. Any further cooling usually results in the formation of dew or frost. Also called dewpoint temperature. When this temperature is below 0 C.. it is sometimes called the frost point. 

FIGURE 8.9 The phase diagram for water and the cooling curve for a sample initially at point A. The sample cools at constant pressure through B to ice at C. The pause in the decline of the cooling curve at B is due to the release of heat when the liquid freezes. 

When a vapor is cooled at constant pressure, it follows a path represen on Fig. 13.15 by a vertical line. Several such lines are shown. If one starts point k, the vapor first reaches its dew point at line BE and then its bubble at line BD, where condensation into single liquid phase ft is complete. This the same process that takes place when the species are completely miscible one starts at point n, no condensation of the vapor occurs until- temperature is reached. Then condensation occurs entirely at this temperature, producing two liquid phases represented by points C and D. If one starts at an intermedi point m, the process is a combination of the two just described. After the point is reached the vapor, tracing a path along line BE, is in equilibrium wi... 

The system water(l)/ n-pentane(2)/n-hexane(3) exists as a vapor at 101.33 kPa and 100°C with mole fractions z, = 0.4S, zi = 0.25, z3 = 0.30. The system is slowly cooled at constant pressure until it is completely condensed into a water phase and a hydrocarbon phase. Assuming that the two liquid phases are immiscible, that the vapor phase is an ideal gas, and that the hydrocarbons obey Raoult s law, determine ... 

Methyl ethyl ketone (MEK) is to be recovered from a gas mixture containing 20.0 mole% MEK and 80.0 mole% at 85 C and 3.5 atm. In a proposed process design, a stream of this mixture is fed to a condenser at a rate of 500 Us and is cooled at constant pressure, causing most of the MEK to condense. 

If a gas containing a single superheated vapor is cooled at constant pressure, the temperature at which the vapor becomes saturated is referred to as the dew point of the gas. From Raoult s law (Equation 6.3-1),... 

The bubble-point temperature of a liquid mixture is the temperature at which the first vapor bubble forms if the mixture is heated at constant pressure. Contrary to what many students mistakenly assume, the bubble point is not the boiling temperature of the most volatile species in the liquid it is always higher than this temperature for an ideal liquid solution. The dew-point temperature of a vapor mixture is the temperature at which the first liquid droplet forms if the mixture is cooled at constant pressure. If Raoult s law applies to all species, either of these temperatures can be determined by trial and error using Equation 6.4-4 (for the bubble point) or Equation 6.4-7 (for the dew point). 

In an acetone-recovery process, a gas stream containing 20.0 mole% acetone and the remainder nitrogen leaves a chemical plant at 90°C and 1 atm. The stream is cooled at constant pressure in a condenser, enabling some of the acetone vapor to be recovered as a liquid. The nitrogen and uncondensed acetone are discharged to the atmosphere. 

Dew point, Tjp—the temperature at which humid air becomes saturated if it is cooled at constant pressure. 

Dew point (of a gas mixture) The temperature at which the first liquid droplet appears when the mixture is cooled at constant pressure. 

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