calorimetry

[Latin calor, heat; see caloric + -METRY.]

The measurement of the quantity of heat energy involved in processes such as chemical reactions, changes of state, and mixing of substances, or in the determination of heat capacities of substances. The unit of energy in the International System of Units is the joule. Another unit still being used is the calorie, defined as 4.184 joules.

A calorimeter is an apparatus for measuring the quantity of heat energy released or absorbed during a process. Since there are many processes that can be studied over a wide range of temperature and pressure, a large variety of calorimeters have been developed.

Nonisothermal calorimeters measure the temperature change that occurs during the process. An aneroid-type nonisothermal calorimeter is normally constructed of a material having a high thermal conductivity, such as copper, so that there is rapid temperature equilibration. It is isolated from its surroundings by a high vacuum to reduce heat leaks. This type of calorimeter can be used for determining the heat capacity of materials when measurements involve low temperatures. Aneroid-type nonisothermal calorimeters have also been developed for measuring the energy of combustion for small samples of rare materials.

With most nonisothermal calorimeters, it is necessary to relate the temperature rise to the quantity of energy released in the process. This is done by determining the calorimeter constant, which is the amount of energy required to increase the temperature of the calorimeter itself by 1°. This value can be determined by electrical calibration or by measurement on a well-defined test system. For example, in bomb calorimetry the calorimeter constant is often determined from the temperature rise which occurs when a known mass of a very pure standard sample of benzoic acid is burned.

Isothermal calorimeters make measurements at constant temperature. The simplest example is a calorimeter containing an outer annular space filled with a liquid in equilibrium with a crystalline solid at its melting point, arranged so that any volume change will displace mercury along a capillary tube. The Bunsen ice calorimeter operates at 0°C (32°F) with a mixture of ice and water. Changes as a result of the process being studied cause the ice to melt or the water to freeze, and the consequent volume change is determined by measurement of the movement of the mercury meniscus in the capillary tube. While these calorimeters can yield accurate results, they are limited to operation at the equilibrium temperature of the two-phase system. Other types of isothermal calorimeters use the addition of electrical energy to achieve exact balance of the heat absorption that occurs during an endothermic process.

All calorimeters consist of the calorimeter proper and a jacket or a bath, which is used to control the temperature of the calorimeter and the rate of heat leak to the environment. For temperatures not too far removed from room temperature, the jacket or bath contains liquid at a controlled temperature. For measurements at extreme temperatures, the jacket usually consists of a metal block containing a heater to control the temperature. With nonisothermal calorimeters, where the jacket is kept at a constant temperature, there will be some heat leak to the jacket when the temperature of the calorimeter changes. It is necessary to correct the temperature change observed to the value it would have been if there were no leak. This is achieved by measuring the temperature of the calorimeter for a time period both before and after the process and applying Newton's law of cooling. This correction can be avoided by using the technique of adiabatic calorimetry, where the temperature of the jacket is kept equal to the temperature of the calorimeter as a change occurs. This technique requires more elaborate temperature control, and its primary use is for accurate heat capacity measurements at low temperatures.

In calorimetric experiments it is necessary to measure temperature differences accurately; in some cases the temperature itself must be accurately known. Modern calorimeters use resistance thermometers to measure both temperatures and temperature differences, while thermocouples or thermistors are used to measure smaller temperature differences.

Heat capacities of materials and heats of combustion are processes that are routinely measured with calorimeters. Calorimeters are also used to measure the heat involved in phase changes, for example, the change from a liquid to a solid (fusion) or from a liquid to a gas (vaporization). Calorimetry has also been applied to the measurement of heats of hydrogenation of unsaturated organic compounds, the heat of dissolution of a solid in a liquid, or the heat change on mixing two liquids.

The measurement of energy expenditure by the body. Direct calorimetry is the direct measurement of heat output from the body, as an index of energy expenditure, and hence energy requirements. The subject is placed inside a small, thermally insulated room, and the heat produced is measured.

Indirect calorimetry is a means of estimating energy expenditure by either measurement of the rate of oxygen consumption, using a spirometer, (each litre of oxygen consumed is equivalent to 20 kJ energy expenditure) or estimation of the total production of carbon dioxide over a period of 7-10 days, after consumption of dual isotopically labelled water (i.e. water labelled with both ²H and ¹⁸O). See also isotopes.

Measurements of energy expenditure and energy consumption in terms of heat units, usually expressed as kilocalories. There are two main types of calorimetry: direct and indirect.

Direct calorimetry is based on the premise that energy expended by an individual doing any kind of work is ultimately converted to heat. To measure this heat, a person is placed in a specially designed, insulated chamber (called a calorimeter) supplied with air and surrounded by a jacket of circulating water; the heat production (or energy expenditure) is estimated from changes in the temperature of the surrounding water.

Indirect calorimetry uses oxygen consumption as a means of estimating energy expenditure. Oxygen is required to release from food the energy needed for activity. The more energy expended, the more oxygen is consumed. To convert values of oxygen consumption to kilo-calories of energy expenditure, it is necessary to know what type of food is being used as the energy source. This is because a litre of oxygen will release different amounts of energy from fats, carbohydrates, and proteins.

A new method for measuring energy expenditure has been devised. This entails drinking heavy water (it has the formula ²H₂¹⁸O; normal water has the formula ¹H₂¹⁶O). Oxygen-18 and deuterium (hydrogen-2) are two stable, harmless isotopes that can be detected in liquids or in air. Some of the oxygen-18 is exhaled as carbon dioxide (the waste product of respiration), and some is excreted in urine along with some of the deuterium. Deuterium is lost from the body only in water. The difference between the rate of excretion of deuterium and oxygen-18 in the urine over a reasonable length of time (usually a day or more) can be used to estimate energy expenditure. The estimates can be made using daily urine samples and do not affect performance. The method has been used to gain valuable information about true energy expenditure under natural, as opposed to laboratory, conditions. Dual-labelled water was used to show that Sir Ranulph Fiennes and Dr Mike Stroud expended more than 8000 Calories a day during their polar expedition. This is three to four times an average person's daily energy expenditure and double the amount used by riders in the gruelling Tour de France.

The measurement of the amounts of heat radiated and absorbed.

Measurements of energy production and energy consumption in terms of heat. See also direct calorimetry, indirect calorimetry.

Measurement of the heat eliminated or stored in any system.

• direct c. — measurement of heat actually produced by the organism which is confined in a sealed chamber or calorimeter.
• indirect c. — estimation of the heat produced by means of the respiratory differences of oxygen and carbon dioxide in the inspired and expired air.

The world’s first ice-calorimeter, used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in various chemical changes; calculations which were based on Joseph Black’s prior discovery of latent heat. These experiments mark the foundation of thermochemistry.

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. Calorimetry involves the use of a calorimeter. The word calorimetry is derived from the Latin word calor, meaning heat. Scottish physician and scientist Joseph Black, who was the first to recognize the distinction between heat and temperature, is said to be the founder of calorimetry.^[1]

Indirect calorimetry calculates heat that living organisms produce from their production of carbon dioxide and nitrogen waste (frequently ammonia in aquatic organisms, or urea in terrestrial ones), OR from their consumption of oxygen. Lavoisier noted in 1780 that heat production can be predicted from oxygen consumption this way, using multiple regression. The Dynamic Energy Budget theory explains why this procedure is correct. Of course, heat generated by living organisms may also be measured by direct calorimetry, in which the entire organism is placed inside the calorimeter for the measurement.

The specific heat formula is as follows:

where

q is energy, or heat,

m is mass,

c is specific heat,

ΔT is change in temperature.

Constant-volume calorimetry (bomb calorimetry)

Constant-volume calorimetry is calorimetry performed at a constant volume. This involves the use of a constant-volume calorimeter.

No work is performed in constant-volume calorimetry, so the heat measured equals the change in internal energy of the system. The equation for constant-volume calorimetry is (the heat capacity at constant volume is assumed to be constant):

where

ΔU is change in internal energy,

ΔT is change in temperature and

C_V is the heat capacity at constant volume.

Since in constant-volume calorimetry the pressure is not kept constant, the heat measured does not represent the enthalpy change.

References

1. ^ Laider, Keith, J. (1993). The World of Physical Chemistry. Oxford University Press. ISBN 0-19-855919-4. 

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