Systems with uniform temperature

Now assume that we treat a case in which a chemical reaction is occurring in a system with uniform temperature, the first of Eqs. (59) becomes... 

In practice, conditions in a reactor are usually quite different than the ideal requirements used in the definition of reaction rates. Normally, a reactor is not a closed system with uniform temperature, pressure, and composition. These ideal conditions can rarely if ever be met even in experimental reactors designed for the measurement of reaction rates. In fact, reaction rates cannot be measured directly in a closed system. In a closed system, the composition of the system varies with time and the rate is then inferred or calculated from these measurements. 

SYSTEMS WITH UNIFORM TEMPERATURE DISTRIBUTION Semenov assumed a pseudo zero order (that is, with no reactant consumption) exothermic reaction following an Arrhenius type rate law — that is, the rate of reaction and therefore the rate of heat production increa.ses exponentially with temperature. Thus for an irreversible nth order reaction A — B at constant volume V the rate of heat production is given by ... 

Similar relations can be derived for 17 as a function of T, V and Nk-These relations are valid for homogeneous system with uniform temperature and pressure. They can be extended to inhomogeneous systems as long as one can associate a well-defined temperature to every location. The thermodynamics of an inhomogeneous system can be formulated in terms of entropy density s(7 (x),njt(x)), which is a function of the temperature and the mole number densities at the point x. If m(x) is the energy density, then following (4.4.4) we have the relations... 

Nonequilibrium Systems with Uniform and Time-Constant Temperature and Pressure... 

An equivalent form of this statement, which relates it more obviously to practical considerations, is that work cannot be derived by the continuous utilization of the heat contained in a system at uniform temperature. An aeroplane, for example, cannot propel itself with the aid of some device which consumes the heat of the atmosphere in which it moves. If it did so, it would leave the surroundings cooler than itself, and the process could only continue if heat flowed against the adverse temperature gradient so created. 

Interaction of Two Effects Let us consider a simple system with uniform pressure p and temperature T which conform to the values p and T in the surroundings. Moreover, only one reaction may occur inside this system. Now there are three pathways over which the energy content W of the system can be changed ... 

Equation (5.5) deals with properties only. It must be satisfied for changes in state of any closed system of uniform temperature, T, and pressure, P. No restrictions on the mechanical and thermal reversibilities. Equation (5.5) is applicable for incremental changes. It governs the direction of change that leads toward equilibrium. Equation (5.5) may be used for changes between equilibrium states. A corollary to Equation (5.5) at constant entropy and constant volume is... 

In this study, an integrated methanol reformer including an evaporator and a combustor was fabricated and tested. Previous tests of the reformer with a number of on-off cycles revealed that non-uniform temperature distribution caused hot spots within the combustion plate, resulting in cracking of the welded region of the reformer. Therefore, emphasis was made to achieve a uniform temperature distribution within the reformer. In addition, start-up characteristics of the complete reforming system were investigated. 

Figure 2.22 [2.6] demonstrates the method of a cooling circuit with recirculated flow An injector pump operated with just evaporated LN2 aspirates the warmer N2 coming from the condenser and feeds the mixture back in the condenser. The desired condenser temperature can be controlled by a throttle valve. To achieve a uniform temperature distribution, the gas mixture is alternately fed to one or the other end of the condenser. No results of such a system are given. 

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