Adiabatic container

An estimation of the time required for an exothermic reaction, in an adiabatic container, (that is, no heat gain or loss to the environment), to reach the point of thermal runaway. 

Figure 3.9 Schematic representation of (a) an adiabatic container, allowing PV work by movement of a piston, but unaffected by other changes in the surroundings (b) a diathermal (nonadiabatic) container, allowing thermal equilibration with the surroundings.

One g-mole of pure liquid sulfuric acid at temperature To (°C) is mixed with r g-moles of liquid water, also at temperature 7 o(°C). in an adiabatic container. The final solution temperature is 7,( 0). The mass heat capacities of the pure acid, pure water, and the product solution [J/(g C)j are Cpa, and Cps, respectively, all of which may be taken to be constant (independent of temperature). 

As the first application of these criteria, consider the problem of identifying the state of equilibrium in a closed, nonreacting multicomponent system at constant internal energy and volume. To be specific, suppose N moles of species 1, moles of species 2, and so on are put into an adiabatic container that will be maintained at constant volume, and that these species are only partially soluble in one another, but do not chemically react. What we would like to be able to do is to predict the composition of each of the phases present at equilibrium. (A more difficult but solvable problem is to also predict the number of phases that will be present. This problem is briefly considered in Chapter 11.) In the analysis that follows, we develop the equation that will be used in Chapters 10, 11, and 12 to compute the equilibrium compositions. 

Consider the process shown in Figure 10.1 where two ideal gases (originally separated by a partition) mix, forming an ideal solution at fixed total pressure and temperature in an adiabatic container. After mixing, the partial pressure of each gas is given by... 

Sometimes the drop calorimeter and adiabatic methods are combined, and the heated sample is dropped into and adiabatic container. Griskey and Hubbell [77] describe the use... 

Experimental data from an approximately adiabatic container [1] are compared with the theory in Fig. 8, The parameter for comparison is the final spatial mean gas density which is obtained from the equation of state [8] and a mean temperature found by a spatial integration oiT[x,6), (8). Because these data do not involve heat transfer with an amMent they are employed to determine a reasonable value for Ascanbeseen ranges between 1 and 3 Btu/hr-ft - F. It is thought that this range is on the low side and that somewhat increased values... 

The temperature does not change if the perfect gas, enclosed in an adiabatic container, is released in a vacuum. This is because the internal energy U of the perfect gas is simply decided by the temperature, which is kinetic. We can prove this as follows Assume that the perfect gas is contained in a cube with rigid walls of sides L. If the gas molecules undergo elastic collisions at the rigid wall in the x-direction and the mean velocity of the molecules is w, the change of linear momentum ALM before and after a collision is 2m and the mean free path is 2L, the mean number of collisions Ncoi per unit time against the wall is w/2L. Thus the pressure of the wall area V- can be calculated by... 

We isolate the system by enclosing it in a rigid, stationary adiabatic container. The constraints needed to isolate the system, then, are given by the relations... 

A tall column of gas whose intensive properties are a function of elevation may be treated as an infinite number of uniform phases, each of infinitesimal vertical height. We can approximate this system with a vertical stack of many slab-shaped gas phases, each thin enough to be practically uniform in its intensive properties, as depicted in Fig. 8.1. The system can be isolated from the surroundings by confining the gas in a rigid adiabatic container. In order to be able to associate each of the thin slab-shaped phases with a definite constant elevation, we specify that the volume of each phase is constant so that in the rigid container the vertical thickness of a phase cannot change. 

FIGURE 3.4 If we place a suitable amount of pure H2O in a rigid adiabatic container and wait for equilibrium, we will eventually find steam and liquid water, both at the same temperarnre and pressure (except for the very small pressure differences caused by gravity and surface tension). 

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