Calorimetry

Calorimetry is the measurement of heat transfer linked to changes in a body's state—such as chemical reactions, physical changes, or phase transitions—under specific conditions. The term comes from Latin *calor* (heat) and Greek *metron* (measure). The device used is a calorimeter. Joseph Black, a Scottish physician and scientist, is credited as the founder of calorimetry for being the first to distinguish between heat and temperature.

Indirect calorimetry estimates the heat produced by living organisms by measuring their oxygen consumption or their output of carbon dioxide and nitrogen waste (often ammonia in aquatic life or urea in terrestrial animals). In 1780, Antoine Lavoisier showed that heat production could be predicted from oxygen use through multiple regression. The dynamic energy budget theory explains why this method is valid. Direct calorimetry, in contrast, measures heat by placing the entire organism inside a calorimeter. A modern tool is the differential scanning calorimeter, which heats a small sample at a controlled rate and records the heat flow into or out of the material.

The study of heat dates back over 2,500 years. In the Graeco-Roman era, Plato and Aristotle saw heat as a form of fire. Isaac Newton thought it spread via vibrations of aether particles, while René Descartes described it as accelerated motion of air particles caused by light. Robert Hooke viewed heat as a property of matter from the motion of its parts. For centuries, the dominant theory treated heat as a weightless, self-repelling fluid called "caloric."

Quantitative heat measurement began about three centuries ago. In 1750, Georg Wilhelm Richmann formulated the first general calorimetric equation—Richmann's law—for calculating the equilibrium temperature when mixing similar substances. A decade later, Joseph Black made a key discovery in 1761: adding heat to ice at its melting point or to boiling water did not change their temperature. His identification of latent and specific heat marked the birth of thermodynamics and the separation of heat from temperature.

In 1782, Antoine Lavoisier and Pierre-Simon de Laplace built the first ice-calorimeter, launching quantitative calorimetry. Using Joseph Black's recent method for measuring carbon dioxide, they found that both carbon combustion and respiration (tested with a guinea pig) produced carbon dioxide and water. They assumed the energy to form these products was consistent with the same reactants and products, foreshadowing Hess's law. (In reality, respiration follows a different path—carbon and water form CO₂ in the Krebs cycle, and oxygen is decomposed by iron and copper in the electron transport chain to accept hydrogens—but this was unknown for another 200 years. At least one recent publication has questioned this calorie-metabolism theory.)

Lavoisier credited de Laplace with the ice-calorimeter concept in his 1789 book *Elements of Chemistry*, often considered the first chemistry textbook. In its first chapter, Lavoisier defined "caloric" as the cause of heat, an elastic fluid that separates matter's particles, without requiring it to be a real substance. The ice-calorimeter was initially called "the machine" until the word "calorie" was coined in 1789. The next major advance came from Sir Benjamin Thompson in the 1790s, who observed heat from cannon boring underwater and concluded heat must be a form of energy, not a material. James Prescott Joule quantified this in the 1840s, using falling weights to drive a paddle in insulated liquid and showing that 4.184 joules of work produce the same heating as one calorie, linking mechanical work to thermal energy. Around 1840, Germain Henri Hess formulated Hess's law, stating that a chemical reaction's total enthalpy change is independent of the reaction path—a principle still fundamental to thermochemistry and calorimetry. In the 1870s, Pierre Eugène Berthelot developed the first modern bomb calorimeter and introduced the concepts of endothermic and exothermic reactions.

Classical calorimetric calculation of heat involves cases with a differentiable equation of state for a one-component body. A basic classical calculation with respect to volume requires a reference material with known thermal constitutive properties. The classical rule, recognized by Clausius and Kelvin, is that the pressure exerted by the material follows a defined relationship.