Calorimetry

Calorimetry is the experimental technique for QUANTITATIVELY measuring heat exchange, carried out using a calorimeter (Fig. 7.8) -- typically a cylindrical vessel made of copper or aluminium, fitted with a stirrer and a lid, and well insulated so that essentially no heat is exchanged with the surroundings outside the vessel itself. Because the system (calorimeter + its contents) is effectively isolated, the principle of conservation of energy applies directly: any heat LOST by one part of the system must be exactly GAINED by the rest -- "heat gained equals heat lost."

The standard technique built on this principle is the METHOD OF MIXTURES: a sample 'A' of the substance under study is heated to an accurately known high temperature, then quickly transferred into the calorimeter (which already contains water at a known lower temperature), and the mixture is stirred continuously until it settles at a common final temperature. All the heat lost by the cooling sample 'A' is gained by the water and by the calorimeter (and stirrer) itself.

Writing $m_1, s_1, T_1$ for the sample's mass, specific heat and initial temperature; $m_2, s_2$ for the calorimeter+stirrer's mass and specific heat; $m_3, s_3$ for the water's mass and specific heat; $T_2$ for the initial (common) temperature of calorimeter+water; and $T$ for the final common temperature, conservation of energy gives:

Knowing the specific heats of water ($s_3 = 4186\text{ J kg}^{-1}\text{K}^{-1}$) and of the calorimeter material (e.g. copper, $s_2 = 387\text{ J kg}^{-1}\text{K}^{-1}$), this can be solved for the UNKNOWN specific heat $s_1$ of the sample:

$s_1 = \frac{(m_2 s_2 + m_3 s_3)(T - T_2)}{m_1(T_1 - T)} \quad \text{--- (7.31)}$ …