Cooling isobaric

Let us consider a volume of moist air that is cooled isobarically. Assuming that we can neglect mass exchange between the air parcel and its surroundings, the water vapor partial pressure (pw) will remain constant. A temperature decrease from an initial value 7o to Td will lead to a decrease of the saturation vapor pressure from p°(7b) to p°(Td). 

We would like to calculate when the parcel will become saturated. In other words, if a parcel initially has a temperature 7b and relative humidity RH (from 0 to 1), what is the temperature Td at which it will become saturated (RH = 1) The temperature Td is called the dew temperature or dewpoint. 

Td can be calculated recognizing that by definition RH = Pw/p° To) and that at the dew point pw = p°(Td). The dependence of the saturation vapor pressure on temperature is given by the Clausius-Clapeyron equation (17.8). Integration between 7o, P°(Tq), and Td, p, yields 

Assuming that the latent heat AHv is approximately constant from 7b to Td, we get 

2 The classic Kohler formulation does not consider the cases of solutes that are not completely soluble or soluble gases, both of which influence the solute effect term in (17.27). In such cases cloud droplets can exist at S 1 since B/D A/Dp. 

Noting that the ratio on the left-hand side is equal to the initial relative humidity, and assuming that the temperature change is small enough so that Tq Td — Tq, we get 

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The point on the pvT diagram at which the final isobaric cooling begins (4), controls the total part shrinkage. This point is influenced by the two main processing conditions —the melt temperature and the holding pressure as depicted in Fig. 3.43. 

An ideal gas at 50°C and 1 atm is heated to 500°C at constant pressure, and then isothermally compressed to 10 atm. It is then isobarically cooled to 50°C, and finally is isothermally expanded to back to its initial state. For the overall process, determine AH and AU. 

XII (long dashed lines) and extrapolated equilibrium lines at low temperatures (short dashed lines). Hydrogen ordered ices XIII and XIV were prepared by isobaric cooling of HCl (DCl) doped H2O (D2O) ice V or XII to 77 K at 0.5 GPa or 1.2 GPa, respectively (indicated by arrows). Cooling of ice XII w as started at 190 K, which is 10 K below the temperature where transition to stable ice VI would occur. The temperatures of the hydrogen ordering phase transitions are indicated by grey bars. Transition temperatures for ice V ice... 

In a temperature vs. entropy diagram (Rankine diagram), we are able to see the four steps to liquefy a gas in the case of the Linde cycle. Figure 23.7 shows the starting gas g at experiments under isobaric conditions, a heating in a counterflow heat exchanger in (1). Secondly, it is compressed isothermically to (2) and then from (2) to (3) it is isobarically cooled in a counterflow... 

The Claude s cycle is a nonideal isentropic plus an isenthalpic expansion. A preheated gas is firstly isothermally compressed from p to p2 followed by a fast isobaric cooling through 3 from T 300 K. There, an expansion engine with another precooled gas helps the hydrogen gas to step to point 4 and then to T2 80 K. An expansion valve helps the cooled gas to go isenthalpically to point 5 at an even lower temperature T3 30 K and p3 being lower than p2. An isentropic expansion finally produces the liquefied gas at the initial T. ... 

If a liquid and a vapor are initially present and if, upon isobaric cooling, a solid falls out of solution, an SLG point is obtained. But if all the liquid in the... 

Figure 3. Schematic behavior of enthalpy and isobaric heat capacity of a glass-forming liquid subject to isobaric cooling and subsequent reheating at a constant rate through the glass transition region. The two temperatures TA and TB correspond to two different values obtained for the glass transition temperature Tg for different rates. (Reproduced from Ref. 19.)...

Path C. A compression in which PV" = constant, where ) isobaric cooling or heating, if necessary, to 300°C. 

An unsaturated or saturated vapor may become supersaturated by undergoing various thermodynamic processes, such as isothermal compression, isobaric cooling, and adiabatic expansion. In the first of these processes the vapor temperature remains constant, whereas it decreases in the latter two processes. 

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