Heat of temperatures

Alpert Y, Jerby E (1999) Coupled thermal-electromagnetic model for microwave heating of temperature-dependent dielectric media. IEEE Trans Plasma Sci 27 555-562... 

The heat capacity of an ideal vapor is a monotonic function of temperature in this work it is expressed by the empirical relation... 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

As the amount of temperature cross increases, however, problems are encountered, as illustrated in Fig. 7i8c. Local reversal of heat flow may be encountered, which is wasteful in heat transfer area. The design may even become infeasible. 

Example 9.1 A process involves the use of benzene as a liquid under pressure. The temperature can be varied over a range. Compare the fire and explosion hazards of operating with a liquid process inventory of 1000 kmol at 100 and 150°C based on the theoretical combustion energy resulting from catastrophic failure of the equipment. The normal boiling point of benzene is 80°C, the latent heat of vaporization is 31,000 kJ kmol the specific heat capacity is 150 kJkmoh °C , and the heat of combustion is 3.2 x 10 kJkmok. ... 

Adiabatic operation. If adiabatic operation leads to an acceptable temperature rise for exothermic reactors or an acceptable fall for endothermic reactors, then this is the option normally chosen. If this is the case, then the feed stream to the reactor requires heating and the efiluent stream requires cooling. The heat integration characteristics are thus a cold stream (the reactor feed) and a hot stream (the reactor efiluent). The heat of reaction appears as elevated temperature of the efiluent stream in the case of exothermic reaction or reduced temperature in the case of endothermic reaction. 

The first distinction to be drawn, as far as heat transfer is concerned, is between the plug-flow and continuous well-mixed reactor. In the plug-flow reactor shown in Fig. 13.1, the heat transfer can take place over a range of temperatures. The shape of the profile depends on... 

Figure 13.1a shows two possible thermal profiles for exothermic plug-fiow reactors. If the rate of heat removal is low and/or the heat of reaction is high, then the temperature of the reacting stream will increase along the length of the reactor. If the rate of heat removal is high and/or the heat of reaction is low, then the temperature will fall. Under conditions between the two profiles shown in Fig. 13.1a, a maximum can occur in the temperature at an intermediate point between the reactor inlet and exit. 

If indirect heat transfer is used with a large temperature difference to promote high rates of cooling, then the cooling fluid (e.g., boiling water) is fixed by process requirements. In this case, the heat of reaction is not available at the temperature of the reactor effluent. Rather, the heat of reaction becomes available at the temperature of the quench fluid. Thus the feed stream to the reactor is a cold stream, the quench fluid is a hot stream, and the reactor effluent after the quench is also a hot stream. 

Figure 13.5 shows a flowsheet for the manufacture of phthalic anhydride by the oxidation of o-xylene. Air and o-xylene are heated and mixed in a Venturi, where the o-xylene vaporizes. The reaction mixture enters a tubular catalytic reactor. The heat of reaction is removed from the reactor by recirculation of molten salt. The temperature control in the reactor would be diflficult to maintain by methods other than molten salt. 

The appropriate placement of reactors, as far as heat integration is concerned, is that exothermic reactors should be integrated above the pinch and endothermic reactors below the pinch. Care should be taken when reactor feeds are preheated by heat of reaction within the reactor for exothermic reactions. This can constitute cross-pinch heat transfer. The feeds should be preheated to pinch temperature by heat recovery before being fed to the reactor. 

Both the reboiling and condensing processes normally take place over a range of temperature. Practical considerations, however, usually dictate that the heat to the reboiler must be supplied at a temperature above the dew point of the vapor leaving the reboiler and that the heat removed in the condenser must be removed at a temperature lower than the bubble point of the liquid. Hence, in preliminary design at least, both reboiling and condensing can be assumed to take place at constant temperatures. ... 

The heat input to diyers is to a gas and as such takes place over a range of temperatures. Moreover, the gas is heated to a temperature higher than the boiling point of the liquid to be evaporated. The exhaust gases from the dryer will be at a lower temperature than the inlet, but again, the heat available in the exhaust will be available over a range of temperatures. The thermal characteristics of dryers tend to be design-specific and quite difierent in nature from both distillation and evaporation. 

Dryers are different in characteristic from distillation columns and evaporators in that the heat is added and rejected over a large range of temperature. Changes to dryer design can be directed by the plus/minus principle. 

British thermal unit (Btu) The most commonly used industrial heal unit the amount of heat required to raise 1 lb of water through UF under specified conditions. Since the specific heat of water varies, particularly with temperature, the actual value of Btu is dependent on the conditions chosen as stan-... 

Dulong and Pedt s law The product of the atomic weight and the specific heat of a metal is constant of value approximately 6-2. Although not true for all metals at ordinary temperatures, these metals and several non-metals approximate to the law at high temperatures. 

Using this equation it is possible to calculate heats of reaction from the variation of AG with temperature. 

For pure organic materials, it is also possible to calculate the heating value starting from the heats of formation found in tables of thermodynamic data. The NHV is obtained using the general relation of thermochemistry applicable to standard conditions of pressure and temperature (1 bar and 25°C)) f 9j... 

Fuel passing through certain hot zones of an aircraft can attain high temperatures moreover it is used to cool lubricants, hydraulic fluids, or air conditioning. It is therefore necessary to control the thermal stability of jet fuels, more particularly during supersonic flight where friction heat increases temperatures in the fuel tanks. 

Triple point temperature K Heat of fusion kJ/lc Heat of vaporization kJ/kg Liquid conductivity atr, W / (m-K) Liquid conductivity AtT W/(m-I0 Temperature Ti K Temperature h K... 

Triple point temperature Heat of fusion Heat of vaporization Liquid conductivity at r, Liquid conductivity at Temperature Tx Temperature Tz... 

Triple point Heat of Heat of Liquid liquid Temperature Temperature... 

The most important factor for maturation and hydrocarbon type is therefore heat. The increase of temperature with depth is dependent on the geothermal gradient which varies from basin to basin An average value is about 3°C per 100 meters of depth. 

Knowledge of the temperature coefficient of 0 provides a means of calculating the heat of immersion. Differentiation of Eq. X-18 yields... 

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