Calorimetry determines an energy change by measuring the temperature change of matter with a known heat capacity.

If a body of mass $m$ and specific heat capacity $c$ changes temperature by $\Delta T$, then for ordinary sensible heating

$$q=mc\Delta T.$$

A calorimeter itself may also absorb energy. If its total heat capacity is $C_{\mathrm{cal}}$,

$$q_{\mathrm{cal}}=C_{\mathrm{cal}}\Delta T.$$

The essential principle is an energy balance. If the calorimeter and its contents are sufficiently isolated from the external environment, energy released by one part is absorbed by the others:

$$\boxed{q_{\mathrm{process}}+q_{\mathrm{surroundings}}=0}.$$

Thus

$$q_{\mathrm{process}}=-q_{\mathrm{surroundings}}.$$

Example

Suppose a process warms $100.0,\mathrm g$ of water from $22.0,^\circ\mathrm C$ to $28.0,^\circ\mathrm C$. Using

$$c=4.18,\mathrm{J,g^{-1},K^{-1}},$$

its temperature change is

$$\Delta T=6.0,\mathrm K.$$

The water absorbs

$$q_{\mathrm{water}}=mc\Delta T =(100.0)(4.18)(6.0) \approx2.51\times10^3,\mathrm J.$$

Neglecting the calorimeter's own heat capacity,

$$q_{\mathrm{process}}=-2.51,\mathrm{kJ}.$$

The negative sign means the measured process released energy to the water.

A coffee-cup calorimeter operates approximately at constant pressure and is useful for processes occurring in liquids. A rigid bomb calorimeter operates at constant volume and prevents pressure-volume expansion of the calorimeter contents. These different constraints matter when the measured heat is later related to particular thermodynamic state changes.

Real calorimetry may require corrections for the calorimeter's heat capacity, heat leakage, evaporation or incomplete transformation. The conceptual core remains the same: infer an otherwise inaccessible process energy from a measured temperature change and conservation of energy.