Of subcooled liquids

For temperatures below the vapor—liquid critical temperature, T, isotherms to the left of the liquid saturation curve (see Fig. 3) represent states of subcooled liquid isotherms to the right of the vapor saturation curve are for superheated vapor. For sufficiently large molar volumes, V, all isotherms are approximated by the ideal gas equation, P = RTjV. Isotherms in the two-phase liquid—vapor region are horizontal. The critical isotherm at temperature T exhibits a horizontal inflection at the critical state, for which... 

This figure is another example of a phase diagram, drawn here for a constant pressure of 70 kPa. The t - y, curve represents states of saturated vapor, with states of superheated vapor lying above it The t — x, curve represents states of saturated liquid, with states of subcooled liquid lying below iL The two-phase region lies between these curves. 

With reference to the txy diagram, we describe the course of a constant-pressure heating process leading from a state of subcooled liquid at point a to a state of superheated vapor at point d. The path shown on the figure is for a constant composition of 60 mole percent acetonitrile. The temperature of the liquid increases as the result of heating from point a to point b, where the first bubble of vapor appears. Thus point b is a bubble point, and the t - x, curve is the locus of bubble points. 

Vader, D.T., Chrysler, G.M., Chu, R.C. and Simons, R.E., 1995, Experimental Investigation of Subcooled Liquid Nitrogen Impingement Cooling , IEEE Transactions on Components and Packaging Technologies, Part A, Vol. 18(4), pp.788-794... 

One luuidred kmol per hour of subcooled liquid at 300 K and 3 bar is superheated to 500 K in a steady-flow heat exchanger. Estimate tlie exchanger duty (in kW) for one of tile following ... 

Condensation of vapor occurs in a variety of engineering applications. For example, when a vapor is cooled below its saturation temperature, or when a vapor-gas mixture is cooled below its dew point, homogeneous condensation occurs as a fog or cloud of microscopic droplets. Condensation also occurs when vapor comes in direct contact with subcooled liquid such as spraying a fine mist of subcooled liquid droplets into a vapor space or injecting vapor bubbles into a pool of subcooled liquid. The most common type of condensation occurs when a cooled surface, at a temperature less than the local saturation temperature of the vapor, is placed in contact with the vapor. Vapor molecules that strike this cooled surface may stick to it and condense into liquid. 

From enthalpy calculations of subcooled liquid, saturated liquid, saturated vapor, and superheated vapor, Fig. 3.26 is constructed. 

Both mechanisms and their combination have a similar linear relationship between log Kp and the logarithm of subcooled liquid vapor pressure P (Pankow and Bidleman 1992 Pankow 1994), i.e.,... 

Chugging instability occurs when the liquid is heated well above its saturation temperature. When vapor formation eventually occurs, it does so very rapidly and may expel liquid in both directions. The vapor formed can thus enter a region of subcooled liquid where it can collapse violently. This situation can normally occur only at rather low heat fluxes. 

As mentioned before, POP transport in the environment depends on their physicochemical properties [40-54], and these include saturated vapor pressure, solubility, Henry s law constant, octanol-water, octanol-air, and organic carbon-water partition coefficients. The saturated vapor pressure characterizes the capability of a substance to be transferred to the gaseous state. Eollowing the study of Wania and Mackay [40], the efficiency of POP condensation with subcooled liquid pressure (p°L) at 25°C above 1 Pa is very low. POPs with a vapor pressure between 1 and 10" Pa are condensed at a temperature of about -30°C and their deposition may be expected mostly in the polar latitudes. POPs with a vapor pressure of subcooled liquid from 10" to 10" Pa are condensed at a temperature above 0°C and they may reach to the middle latitudes. EinaUy, POPs of low volatility with a vapor pressure of subcooled liquid below 10" Pa are practically not vaporized and these substances may be transported and deposited as fine aerosols or coarse particles [39]. Using the vapor pressure of the subcooled liquid it is possible to characterize the partitioning of a POP between the gas phase and the solid phase of the atmospheric aerosol. The POPs having a lower vapor pressure are better bound with... 

Commercial grade propane was utilized for both the jet fire fuel and tank contents. Vessel fills of 20, 41, 60, and 85 volume percent were examined under jet fire attack of the ignited flashing discharge of subcooled liquid propane at about 0.9 MPa. 

Besides providing feasible computer routes to handle the three aforementioned problems, special care must be taken to prevent the computer flash algorithm from oscillating back and forth in K constant (vapor-liquid equilibrium) calculations because the prescribed flash conditions of temperature and pressure do not fall in the two-phase region. It would be presumptuous to assume that all flash conditions are realistic engineers do, and will continue to, submit unrealistic temperature and pressures, in the range of subcooled liquids and superheated vapors. 

Feed enthalpy is identified as the fraction of the feed that is vaporized. Liquid at its boiling point has an enthalpy of 0, while that of saturated vapor is 1.0. The enthalpy of subcooled liquid is negative, that of super heated vapor exceeds 1.0. If no heat were added to or removed from the vapor stream until it entered the condenser, its flow into the con denser would equal that immediately above the feed tray. In this case,... 

If it is desired to have single phase of subcooled liquid at the line terminus, the point 3 must be in the liquid region ... 

If you are very careful to use very pure water, and to exclude all crystallization nuclei, it is possible to subcool liquid water to temperatures far below its equilibrium freezing point (see Figure 5.8). a. Estimate the vapor pressure of subcooled liquid water at — 10°C, using the Clausius-Clapeyron equation, starting at the triple poinL at which point... 

In the previous problem you compared the vapor pressure of ice at — 10°C (=14°F) to that of subcooled liquid water at the same temperature. Using values from that problem, your thermodynamics textbook, or any other source you like, estimate by how much subcooled liquid water at — 10°C wiU increase or decrease its Gibbs energy when it changes to ice at the same temperature. 

From Table I, the specific volume of saturated water vapor with respect to ice at 5 F is 11 550 fl /lb from which IF , jp = 0.000 086 6, but the observed water dew point was in equilibrium with subcooled liquid water at 5 F. From Table I (data from International Critical Tables ), the vapor pressures of subcooled liquid water and of ice at 5 F (-15 C) are 1.436 mm and 1.241 mm Hg, respectively. 

Since the vapor pressure of subcooled liquid water is greater than ice at the same temperature, the weight per cubic foot of water vapor in equilibrium with liquid water will be proportionately larger than the value calculated from the specific volume read from the table, which is for equilibrium with ice. 

Determine the mass of 1 L of saturated liquid water at 25°C. How do you think this value compares to the mass of IL of subcooled liquid water at 25°C and atmospheric pressure ... 

By comparison with Fig. 12.3-2, we see that = 1 if the feed is a saturated liquid. Similarly, q equals zero if the feed is a saturated vapor. However, for feeds that are subcooled liquids or superheated vapors, we need a more complete energy balance. For a feed of subcooled liquid, we recognize that... 

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