Phase equilibrium piston

In our consideration of phase equilibria at constant pressure, we imagined the overall system confined by a piston. However, when we talk about constant-pressure systems, we usually mean that the pressure is maintained by an inert gas (e.g., the atmosphere).2 In some situations, much higher constant pressures of inert gases are applied to systems. If we take a gas-condensed phase equilibrium and apply an inert gas pressure to both phases, we get, from Eqs. (31) and (33),... 

The schematic diagram of the high-pressure vapor-liquid equilibrium circulation-type apparatus is shown in Fig.l. The main piece of the equipment is a high-pressure phase equilibrium cell of approximately 100 cm3. The apparatus includes a compressed-air actuated piston-pump that allows to circulate one or both phases to bring the vapor and liquid in close contact with each other. This pump, the cell and all the related valves were placed in a constant-temperature water bath to have and to keep uniformely the desired temperature. 

Consider the problem of phase equilibrium as shown in Figure 3.5. For the hydrogen-oxygen system described above, we probably have only one phase, but we can consider other systems in which more phases are present in which we have replaced the constant temperature and pressure constraints of Figure 3.5 with adiabatic, constant-volume restrains. The analogous situation would be Figure 3.5 with the piston firmly fixed in place and the walls of the container changed to perfect insulators. 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

The nature of the phase rule can be induced from some simple examples. Consider the system represented in Figure 24-3. It is made of water-substance (water in its various forms), in a cylinder with movable piston (to permit the pressure to be changed), placed in a thermostat with changeable temperature. If only one phase is present both the pressure and the temperature can be arbitrarily varied over wide ranges the variance is 2. For example, liquid water can be held at any temperature from its freezing point to its boiling point under any applied pressure. But if two phases are present the pressure is automatically determined by the temperature, and hence the variance is reduced to 1. For example, pure water vapor in equilibrium with water at a given temperature has a definite pressure, the vapor pressure of water at that temperature. And if three phases are present in equilibrium, ice, water, and water vapor, both the temperature and the pressure are exactly fixed the variance is then 0. This condition is called the triple point of ice, water, and water vapor. It occurs at temperature +0.0099 C and pressure 4.58 mm of mercury. 

Different kinds of driving forces tend to bring about different kinds of change. For example, imbalance of meehanical forces such as pressure on a piston tend to cause energy transfer as work temperature differences tend to eause the flow of heat gradients in chemical potential tend to cause substances to be transferred from one phase to another. At equilibrium all sueh forees are in balance. 

For example, suppose I put just water in the piston at 1 atm and room temperature (say 70 °F) Just one component — no air Is the water liquid, solid, or vapor We know from our own experience that water is a liquid near room temperature. Thus we have just one phase present at equilibrium. ... 

For example, in dry climates (low humidity), snow and ice seem to sublime— a minimum amount of slush is produced. Wet clothes put on an outside line at temperatures below 0°C freeze and then dry while frozen. However, the phase diagram (Fig. 16.55) shows that ice should not be able to sublime at normal atmospheric pressures. What is happening in these cases Ice in the natural environment is not in a closed system. The pressure is provided by the atmosphere rather than by a solid piston. This means that the vapor produced over the ice can escape from the immediate region as soon as it is formed. The vapor does not come to equiHbrium with the solid, and the ice slowly disappears. Sublimation, which seems forbidden by the phase diagram, does seem to occur under these conditions, but it is not sublimation under equilibrium conditions. 

Consider two systems, 1 and 2. System 1 is a one-phase mixture of C components, with mole numbers N. This mixture fills a rigid vessel of volume Vj, and the vessel is immersed in a heat bath maintained at temperature Tj. System 2 is another sample of the same mixture, having the same C components and the same mole numbers N. System 2 fills the cylinder of a piston-cylinder apparatus. The cylinder is immersed in a heat bath at T2. A constant external pressure is imposed on the mixture at equilibrium the system pressure P2 balances that external pressure. Therefore, system 2 is at constant pressure, while system 1 is at constant volume. 

Now suppose we exert greater pressure on the piston and compress the gas above the solution, as shown in the middle container in Figure 13.14. If we reduce the gas volume to half its original value, the pressure of the gas increases to about twice its original value. As a result of this pressure increase, the rate at which gas molecules strike the liquid surface and enter the solution phase increases. Thus, the solubility of the gas in the solution increases until equilibrium is again established that is, solubility increases until the rate at which gas molecules enter the Solution equals the rate at which they escape from the solution. Thus, the solubility of a gas in a liquid solvent increases in direct proportion to the partial pressure of the gas above the solution ( FIGURE 13.15). 

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