Principle of Calorimetry

Principle of Calorimetry

Calorimetry is the branch of thermal physics concerned with measuring quantities of heat, and the

whole subject rests on one guiding idea, the principle of calorimetry, which is nothing more than the

law of conservation of energy applied specifically to an isolated system of bodies exchanging heat only

among themselves.

The principle

Suppose two or more bodies, initially at different temperatures, are brought into thermal contact inside

a container that is well insulated from the outside world, so that (ideally) no heat at all escapes to,

or enters from, the surroundings. Heat then flows spontaneously from the hotter body (or bodies) to the

colder one (or ones), and this flow continues until every part of the system has reached one single,

common final temperature -- thermal equilibrium. Because the system as a whole neither creates nor

destroys energy, and (by assumption) loses none of it to the outside, every joule of heat given up by the

substance(s) that cool down in reaching that common temperature must be gained, in exactly equal measure,

by the substance(s) that warm up:

The calorimeter and why it must be insulated

This is precisely why any real calorimetry experiment is carried out inside a calorimeter -- an

insulated vessel, traditionally a metal container surrounded by an insulating jacket (often with a layer

of trapped air or another poor conductor) -- rather than in an open container. If heat were allowed to

leak out to, or in from, the room, the simple "heat lost = heat gained" balance above would no longer hold

exactly, since some of the heat given up by the hotter substance would have escaped to the room instead of

being fully accounted for by the colder substance's temperature rise, making any calculation based on the

principle unreliable. In practice, the calorimeter vessel itself is either made deliberately

low-mass/thin-walled so that its own heat capacity is negligible compared with the substances placed

inside it, or, where that is not a safe assumption, its own heat capacity ($m_{\text{cal}}c_{\text{cal}}$)

is separately measured beforehand and simply included as one more "substance" in the heat balance,

absorbing or releasing its own share of the heat exchanged.

The method of mixtures

The principle of calorimetry is the working basis of the classic method of mixtures, used to

determine an unknown specific heat capacity experimentally. A measured mass of the substance under test,

at a measured initial temperature, is mixed (inside an insulated calorimeter) with a measured mass of a

reference substance of already-known specific heat capacity (almost always water) at a different measured

initial temperature. The mixture is stirred and allowed to settle to one common final temperature, which …