Condition adiabatic

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

A calorimeter is a device used to measure the work that would have to be done under adiabatic conditions to bring about a change from state 1 to state 2 for which we wish to measure AU= U -U This work is generally done by passing a known constant electric current 3 for a known time t through a known resistance R embedded in the calorimeter, and is denoted by where... 

Proof When the time-deiiendent Schiodinger equation is solved under adiabatic conditions, the upper, positive energy component has the coefficient the dynamic phase factor x C, where... 

The reaction occurs at essentially adiabatic conditions with a large temperature rise at the inlet surface of the catalyst. The predominant temperature control is thermal ballast in the form of excess methanol or steam, or both, which is in the feed. If a plant is to produce a product containing 50 to 55% formaldehyde and no more than 1.5% methanol, the amount of steam that can be added is limited, and both excess methanol and steam are needed as ballast. Recycled methanol requited for a 50—55% product is 0.25—0.50 parts per part of fresh methanol (76,77). 

Some unsaturated ketones derived from acetone can undergo base- or acid-catalyzed exothermic thermal decomposition at temperatures under 200°C. Experiments conducted under adiabatic conditions (2) indicate that mesityl oxide decomposes at 96°C in the presence of 5 wt % of aqueous sodium hydroxide (20%), and that phorone undergoes decomposition at 180°C in the presence of 1000 ppm iron. The decomposition products from these reactions are endothermic hydrolysis and cleavage back to acetone, and exothermic aldol reactions to heavy residues. 

Liquid ethylene oxide under adiabatic conditions requires about 200°C before a self-heating rate of 0.02°C/min is observed (190,191). However, in the presence of contaminants such as acids and bases, or reactants possessing a labile hydrogen atom, the self-heating temperature can be much lower (190). In large containers, mnaway reaction can occur from ambient temperature, and destmctive explosions may occur (268,269). 

Measurement of Performance The amount of useful work that any fluid-transport device performs is the product of (1) the mass rate of fluid flowthrough it ana (2) the total pressure differential measured immediately before and after the device, usually expressed in the height of column of fluid equivalent under adiabatic conditions. The first of these quantities is normally referred to as capacity, and the second is known as head. 

FIG. 23-19 Effectiveness of first-order reactions in spheres under adiabatic conditions (Weisz and Hicks, Chem. Eng. Sci., 17, 26.5 [1962]). 

Accelerating Rate Calorimeter (ARC) The ARC can provide extremely useful and valuable data. This equipment determines the self-heating rate of a chemical under near-adiabatic conditions. It usu-aUy gives a conservative estimate of the conditions for and consequences of a runaway reaction. Pressure and rate data from the ARC may sometimes be used for pressure vessel emergency relief design. Activation energy, heat of reaction, and approximate reaction order can usually be determined. For multiphase reactions, agitation can be provided. 

This result is intuitively correct, since it says that at adiabatic conditions the maximum fuel delivered to the inside gives the maximum heat to be removed by heat conduction, and this gives the maximum inside temperature. Yet this is valid only for static or equilibrium conditions. 

Fig. 9. Stored energy release curves for CSF graphite irradiated at 30°C in the Hanford K reactor cooled test hole [64], Note, the rate (with temperature) of stored energy release (J/Kg-K) exceeds the specific heat and thus under adiabatic conditions self sustained heating will occur.

At the adiabatic condition, Q = 0, as no heat is added to or removed from the system. The heat balance becomes... 

In the ARC (Figure 12-9), the sample of approximately 5 g or 4 ml is placed in a one-inch diameter metal sphere (bomb) and situated in a heated oven under adiabatic conditions. Tliese conditions are achieved by heating the chamber surrounding the bomb to the same temperature as the bomb. The thermocouple attached to the sample bomb is used to measure the sample temperature. A heat-wait-search mode of operation is used to detect an exotherm. If the temperature of the bomb increases due to an exotherm, the temperature of the surrounding chamber increases accordingly. The rate of temperature increase (selfheat rate) and bomb pressure are also tracked. Adiabatic conditions of the sample and the bomb are both maintained for self-heat rates up to 10°C/min. If the self-heat rate exceeds a predetermined value ( 0.02°C/min), an exotherm is registered. Figure 12-10 shows the temperature versus time curve of a reaction sample in the ARC test. 

Adiabatic induction time Induction period or time to an event (spontaneous ignition, explosion, etc.) under adiabatic conditions, starting at operating conditions. 

Adiabatic temperature rise Maximum increase in temperature that can be achieved. This increase occurs when the substance or reaction mixture decomposes or reacts completely under adiabatic conditions. The adiabatic temperature rise follows from ... 

FIGURE 4.1 I Energy balance for an adiabatic conditioning chamber. 

Compressible fluid flow occurs between the two extremes of isothermal and adiabatic conditions. For adiabatic flow the temperature decreases (normally) for decreases in pressure, and the condition is represented by p V (k) = constant. Adiabatic flow is often assumed in short and well-insulated pipe, supporting the assumption that no heat is transferred to or from the pipe contents, except for the small heat generated by fricdon during flow. Isothermal pVa = constant temperature, and is the mechanism usually (not always) assumed for most process piping design. This is in reality close to actual conditions for many process and utility service applications. 

Figure 12-22 is convenient for solving for the temperature rise fector for either polytropic or adiabatic conditions, depending upon whether k or n is used. 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

The chapter by Haynes et al. describes the pilot work using Raney nickel catalysts with gas recycle for reactor temperature control. Gas recycle provides dilution of the carbon oxides in the feed gas to the methanator, hence simulating methanation of dilute CO-containing gases which under adiabatic conditions gives a permissible temperature rise. This and the next two papers basically treat this approach, the hallmark of first-generation methanation processes. 

The experimental realisation of adiabatic conditions is difficult heat is always transferred between the gas and its surroundings by conduction and radiation, and the usual plan is to make the changes of volume occur so rapidly that the heat transfer is negligibly small. 

The experimental data show that the magnitude of the heat capacity (or similarly of the specific heat) under adiabatic conditions decreases regularly with the increase of filler content. This phenomenon was explained by the fact that the macromolecules, appertaining to the mesophase layers, are totally or partly excluded to participate in the cooperative process, taking place in the glass-transition zone, due to their interactions with the surfaces of the solid inclusions. 

Compressibility of a gas flowing in a pipe can have significant effect on the relation between flowrate and the pressures at the two ends. Changes in fluid density can arise as a result of changes in either temperature or pressure, or in both, and the flow will be affected by the rate of heat transfer between the pipe and the surroundings. Two limiting cases of particular interest are for isothermal and adiabatic conditions. 

Flow under adiabatic conditions is considered in detail in the next section, although an approximate result may be obtained by putting k equal to y in equation 4,66 this is only-approximate because equating k to y implies reversibility. 

The rate of flow of gas under adiabatic conditions is never more than 20 per cent greater than that obtained for the same pressure difference with isothermal conditions. For pipes of length at least 1000 diameters, the difference does not exceed about 5 per cent. In practice the rate of flow may be limited, not by the conditions in the pipe itself, but by the development of sonic velocity at some valve or other constriction in the pipe. Care should, therefore, be taken in the selection of fittings for pipes conveying gases at high velocities. 

It will now be shown from purely thermodynamic considerations that for, adiabatic conditions, supersonic flow cannot develop in a pipe of constant cross-sectional area because the fluid is in a condition of maximum entropy when flowing at the sonic velocity. The condition of the gas at any point in the pipe where the pressure is P is given by the equations ... 

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