Definitions

# calorimetry

[kal-uh-rim-i-tree]
calorimetry, 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 a solution (see thermodynamics). A number of different units are used in heat measurement, e.g., the calorie, the British thermal unit (Btu), and the joule. The apparatus used in heat measurement is called a calorimeter. The measurement given by the most common type of calorimeter depends upon the temperature change in a fixed quantity of water (or some other liquid whose heat capacity is known) when heat is transferred between the water and an exothermic or endothermic process. If the temperature change is not too large, then the heat transferred is equal to the heat capacity of the water times the mass of the water times the change in temperature. The accuracy of this method of heat measurement depends on the assumption that all the heat transferred in the process passes into or out of the water in which the temperature change is measured, no heat being lost to the environment and none being absorbed by the walls of the container. The amount of heat given off by the combustion of a fuel can be determined very accurately in the so-called bomb calorimeter, which consists of a combustion chamber (the "bomb") set in another chamber filled with water. Heat generated by combustion of the fuel is transmitted to the water, raising its temperature. The calorie content of food is tested this way. Calorimeters are also employed to measure the energies of elementary particles.

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.

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.

## Types

Calorimetry is performed using one of two methods: constant volume or constant pressure, or constant mass.

### Constant-mass

Constant-mass calorimetry is a calorimetry performed at a constant mass and specific heat.

$q = mc Delta T ,$

where

q is energy, or heat,
m is mass,
c is specific heat,
ΔT is change in temperature.

### Constant-volume

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):

$q = C_V Delta T = Delta U ,$

where

ΔU is change in internal energy,
ΔT is change in temperature and
CV 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.

### Constant-pressure

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

The heat measured equals the change in internal energy of the system minus the work performed:

$q = Delta U - w ,$

Since in constant-pressure calorimetry, pressure is kept constant, the heat measured represents the enthalpy change:

$q = Delta H = H_mathrm\left\{final\right\} - H_mathrm\left\{initial\right\} ,$

This formula is a simplified representative of Hess's Law.