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, measurement of heat and the determination of heat capacity. Heat is evolved in exothermic processes and absorbed in endothermic processes; such processes include chemical reactions, transitions between the states of matter, and the mixing of two substances to form
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an instrument for measuring the quantity of heat that is either evolved or absorbed in the course of a physical, chemical, or biological process. The term “calorimeter” was proposed by A. Lavoisier and P. Laplace (1780).
Modern calorimeters are used in the temperature range from 0.1° to 3500°K and make it possible to measure quantities of heat to an accuracy of 10-2 percent. Calorimeters vary in design, which is determined by the nature and duration of the process being studied, the temperature range in which the measurements are performed, the quantity of heat being determined, and the accuracy required.
A calorimeter designed for measuring the total quantity of heat Q evolved during a process from start to finish is called an integrating calorimeter. A calorimeter for measuring the heat output L and its changes during various stages of the process is called a heat flux meter, or “calorimetric oscillograph.” In accordance with the design of the system and the method of measurement, the following calorimeter types are distinguished: liquid and aneroid calorimeters and single and twin (differential) calorimeters.
A liquid integrating calorimeter, of variable temperature with an isothermal jacket, is used to measure the heat of solution and the heat of chemical reactions. This calorimeter consists of a liquid-filled (usually water) vessel, which contains a chamber where the process under investigation is carried out (“bomb calorimeter”), a stirrer, a heater, and a thermometer. Heat evolved in the chamber is then distributed between the chamber, the liquid, and other parts of the calorimeter, which are collectively called the calorimetric system of the instrument. Changes of state (for example, of temperature) of the calorimetric system make it possible to measure the quantity of heat introduced into the device. The heating of the calorimetric system is measured with a thermometer. The actual measurements are preceded by the calibration of the calorimeter, which consists in the determination of the temperature change of the calorimetric system that results from supplying a known quantity of heat (by the heater or as a result of a chemical reaction occurring in the chamber involving a known quantity of standard material). Calibration yields the calorimeter’s heat value, that is, the coefficient by which the calorimeter’s temperature change measured with the thermometer is to be multiplied in order to determine the quantity of heat introduced into the system. The heat value of such a calorimeter is the heat capacity c of the calorimetric system. Determination of the unknown heat of combustion or of another chemical reaction Q reduces to the measurement of the change in temperature Δt of the calorimetric system, caused by the process being studied: Q = c⋅Δt. The value of Q is usually assigned to the mass of the material present in the calorimetric chamber.
Calorimetric measurements permit the direct determination of only the sum of the heats of the process under investigation and of various secondary processes, such as mixing, evaporation of water, and fracture of the ampul with material. The heat of the secondary processes must be determined experimentally or by calculation and must be omitted from the final result. One of the inevitable secondary processes is the heat exchange between the calorimeter and the surrounding medium through radiation and thermal conductivity. In order to take the secondary processes into account, primarily the heat exchange, the calorimetric system is surrounded by a jacket, the temperature of which is regulated.
The jacket temperature in liquid isothermal calorimeters is maintained at a constant level. The greatest difficulty in determining heats of chemical reactions is not due to problems related to consideration of secondary processes but to problems related to the determination of the completeness of the reaction and the necessity of taking several reactions into account.
In integrating calorimeters of another type, isothermal (constant temperature) calorimeters, the introduced heat does not change the temperature of the calorimetric system but causes changes in the aggregate state of a material that constitutes part of this system (for example, melting of ice in the Bunsen ice calorimeter). The quantity of introduced heat is calculated in this case from the mass of the material that has changed its state of aggregation (for example, the mass of melted ice, which can be measured from the change in volume of the ice-water mixture) and from the heat of phase transition.
Aneroid integrating calorimeters are most frequently used for determining the enthalpy of materials at high temperatures (up to 2500°C). The calorimetric system in calorimeters of this type consists of a block of metal (usually copper or aluminum) with wells for the reaction vessel, the thermometer, and the heater. The enthalpy of the material is calculated as the product of the heat value of the calorimeter and the difference between the increases in temperature of the block measured after dropping into its cavity an ampul with a known quantity of material and then another ampul without the material but heated to the same temperature.
The heat capacities of gases, and sometimes of liquids, are determined in the “labyrinth” flow calorimeters from the temperature difference between the inlet and outlet of a steady-state flow of liquid or gas, from the flow rate, and from the Joule heat emitted by the electric heater of the calorimeter.
In contrast to an integrating calorimeter, a calorimeter working in the heat flow measurement mode must be capable of significant heat exchange in order that the heat quantities introduced into the calorimeter may be rapidly removed and the state of the calorimeter may be determined by the instantaneous value of the thermal flux resulting from the process. The thermal flux of the process is determined from the heat exchange between the calorimeter and its jacket. Such calorimeters, developed by the French physicist E. Calvet (1895-1966), consist of a metal block with channels having cylindrical cells. The process under investigation is allowed to proceed in the cells, whereas the metal block performs the function of the jacket (its temperature is maintained at a constant level to an accuracy of 10”5o-10-6oK). The temperature difference between the cell and the block is measured with a thermopile having up to 1,000 junctions. The heat exchange of the cell and the electromotive force of the thermopile are proportional to the small temperature difference arising between the block and the cell when heat is evolved or absorbed in it. Most often two cells are placed into the block functioning as a differential calorimeter: the thermopiles of each cell have the same number of junctions, and therefore the difference between their electromotive forces permits a direct determination of the difference between the strength of thermal fluxes entering the cells. This method of measurement makes it possible to eliminate the distortion of the quantity being determined by random temperature fluctuations of the block. Two thermopiles are usually mounted on each cell: one of these makes it possible to compensate for the thermal flux of the process under investigation on the basis of the Peltier effect, whereas the second one (indicator) measures the uncompensated part of the thermal flux. In this case, the instrument performs as a differential compensating calorimeter. Such calorimeters are capable of measuring the thermal flux of processes with an accuracy of up to 1 microwatt (μW) at room temperature.
The usual calorimeter names, such as “for chemical reactions,” “bomb calorimeter,” “isothermal,” “ice calorimeter,” or “low-temperature calorimeter,” are historical in origin and indicate mainly the type and range of calorimetric applications, without being either a complete or relative characteristic of the instruments in question.
A general classification may be based on an analysis of three principal variables that determine the measurement methods: temperature of the calorimetric system Tc, temperature of the jacket Tj surrounding the calorimetric system, and the quantity of heat L evolved in the calorimeter per unit time (thermal flux).
Calorimeters with constant Tc and Tj are called isothermal, whereas those with Tc = Tj are called adiabatic. Calorimeters operated at a constant temperature difference Tc — Tj are called calorimeters with constant heat exchange. Tj is constant and Tc is a function of L in isoperibolic calorimeters.
An important factor affecting the final results of measurements is the reliable performance of automatic temperature regulators of the isothermal or adiabatic jackets. In adiabatic calorimeters, the jacket temperature is controlled in such a manner as always to be close to the changing temperature of the calorimetric system. The adiabatic jacket is a light metal screen, equipped with a heater, which decreases the heat exchange to such an extent that the temperature of the calorimeter varies only by several ten thousandths of a degree per minute. This frequently makes it possible to lower the heat exchange during the time span of the calorimetric experiment to an insignificant value, which can be neglected. When necessary, the results of the direct measurements may be corrected for heat exchange, the calculation method of which is based on Newton’s law of heat transfer—the proportionality of the thermal flux between the calorimeter and the jacket to the difference between their temperatures, if this difference is not very large (up to 3°-4°C).
For calorimeters with isothermal jackets, the heat of chemical reactions may be determined with errors up to 0.01 percent. If the calorimeter’s dimensions are small, its temperature varies by more than 2°-3°C, and if the process under study is extended, then the correction for heat exchange in the case of the isothermal jacket may comprise as much as 15-20 percent of the measured quantity, which may limit the accuracy of measurements. It is more appropriate in these cases to use the adiabatic jacket.
Adiabatic calorimeters are used for the determination of the heat capacity of solid and liquid materials in the range from 0.1° to 1000°K. At room temperature as well as at lower temperatures, adiabatic calorimeters, protected by vacuum jackets, are immersed into Dewar vessels, filled with liquid helium, hydrogen, or nitrogen. At elevated temperatures (above 100°C), calorimeters are placed into thermostated electric furnaces.
REFERENCESPopov, M. M. Termometriia i kolorimetriia, 2nd ed. Moscow, 1954.
Skuratov, S. M., V. P. Kolesov, and A. F. Vorob’ev. Termokhimiia, parts 1-2. Moscow, 1964-66.
Calvet, E., and H. Prat. Mikrokalorimetriia. Moscow, 1963. (Translated from French.)
Experimental Thermochemistry, vols. 1-2. New York-London, 1956—62.
V. A. SOKOLOV