Physical chemistry isothermal process

The Isothermal Heat Conduction Calorimeter A Versatile Instrument for Studying Processes in Physics, Chemistry, and Biology 195... 

Physical Chemistry of Solid-Gas Interfaces The process being isothermal dT = 0 leads to dn,... 

Wadsd, L., Smith, A.L., Shirazi, H. et al. (2001) The isothermal heat conduction calorimeter a versatile instrument for studying processes in physics, chemistry, and biology. J. Chem. Educ., 78,1080-1086. 

In most laboratory experiments dealing with the properties of a material or a system the properties are measured under isothermal conditions. Separate experiments are required to measure these same property at different temperatures. In thermal analysis the specified property is measured under a controlled temperature regime. The simplest temperature regime would be that of an isothermal experiment, but in most cases the temperature is raised at a predetermined rate, for example, 10°C per minute. The interpretation then involves the variation of a particular property with both temperature and time. There is, however, a decrease in labor and time which makes such studies especially interesting for industrial applications. With more complicated temperature regimes there is an ability inherent in the method to mimic industrial processes. Industries utilizing thermoanalytical methods are listed in Table 1. The plot of the physical property of the sample recorded as a function of the temperature is said to be a thermal analysis curve. There is still some confusion in the literature about this name, as it was initially applied to the specific technique in which the temperature of a sample was recorded against time as it was cooled down from a particular value. The use of the name in this way persists in physical chemistry textbooks where the name thermal analysis is used for this specific purpose. Other conditions that have to be satisfied in the practice of thermal analysis are as follows. 

There appears to be a disparity in terminology of isotherms between the hydrogeology and chemistry literature. While chemistry textbooks describe adsorption isotherms (e.g., Drever, 1988, p. 362 Stumm and Morgan, 1996, p. 521), the hydrogeology literature uses the term sorption isotherms (e.g., Domenico and Schwartz, 1998, p.299 Fetter, 1999, p. 122 Freeze and Cherry, 1979, p.403). Manuals for popular transport codes also describe sorption isotherms (Zheng, 1990, pp.2-9). According to Sposito (1984), the term adsorption includes all reactions on the two-dimensional solid-water interface physical and chemical adsorption and ion-exchange the term sorption refers to all processes that transfer an ion from aqueous to solid phase. 

For one special case, isothermal reaction at constant density, the set of differential equations comprising the time derivatives of all species concentrations is sufficient to determine the evolution of a system described by a given reaction mechanism for any assumed starting concentrations. While this special case does apply for some experiments of interest in combustion research, it does not pertain to the conditions under which most combustion processes occur. Usually we must expand our set of differential equations so as to describe the effects of chemical reaction on the physical conditions and the effects of changes in the physical conditions on the chemistry. In either case, the evolution of the system is found by numerical integration of the appropriate set of ordinary differential equations with a computer. This procedure is known in the language of numerical analysis as the solution of an initial value problem. 

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