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Calorimetry measures heat transfers. A calorimeter, a calibrated heat capacity and an accounting of unwanted heat transfer connect an observed temperature change to an energy balance, as in heat-engine calorimetry and heat-pump calorimetry.

The central idea is to measure a response that is easier to observe than the transfer itself: a known heat capacity turns a temperature change into an energy estimate. Mixing calorimetry can determine an unknown specific heat capacity, while a chemical reaction can be studied by measuring the response of its surroundings. The useful observable is a change in temperature, together with a stated thermodynamic system boundary; a hot object does not contain a separately conserved store of heat.

For a closed system with unchanged bulk kinetic energy and potential energy, let $Q_{\mathrm{in}}$ be net inward heat and $W_{\mathrm{on}}$ net inward work. The first law of thermodynamics givesIf the boundary includes a hot sample, receiving water and the participating vessel, their mutual heat transfer is internal. With no external input, the total storage change is minus the signed outward heat leakage, not the positive amount transferred from sample to water. A calorimeter calibration with an immersed resistor instead supplies electrical work across this boundary; Joule heating converts it into internal energy. Choosing only the receiving water as the boundary changes which transfers count as external.

The mechanical constraint decides which storage quantity the readout represents. For a closed system at fixed volume, with no other work, $Q_V=\Delta U$. At constant external pressure, with only expansion work $p\Delta V$, $Q_p=\Delta H$, where $H=U+pV$ is enthalpy. Thus the corresponding warming balances use heat capacity at constant volume or heat capacity at constant pressure. Electrical or shaft work must be included separately when present. These endpoint balances do not require the actual exchange to be a reversible thermodynamic process.

A covered cup open to atmospheric pressure approximately realizes the second constraint when escaping material is negligible. A sealed rigid reaction vessel realizes the first; its surrounding water, vessel and immersed parts form the calibrated receiver. The reaction's outward heat equals the receiver's gain only after losses and ignition input have been accounted for. The distinction concerns the reaction boundary, even if its receiver is open to atmospheric pressure.^[ref]

A historical quantitative result appears in James Prescott Joule's On the Mechanical Equivalent of Heat (1850): Table IX gives $772.692$ foot-pounds of mechanical work per warming of one pound of water by one degree Fahrenheit, with weighing reduced to vacuum. His final rounded statement specifies water between $55$ and $60$ degrees Fahrenheit. He acknowledged residual vibration and sound as possible upward bias. This is an original reported conversion result, not the definition of the modern joule; the apparatus and resting controls are described in Joule's paddle-wheel experiment.^[ref]

Joule's paper On the Mechanical Equivalent of Heat (1850) describes a copper vessel holding water and a brass paddle with stationary vanes. Descending lead weights drove its shaft through strings and pulleys; the vanes opposed simple co-rotation. A boxwood shaft segment reduced thermal conduction. He measured fall distances and initial/final temperatures, repeating twenty descents per run and disconnecting the drive for rewinding. Calibrated thermometers read the water and room.^[ref]

His matched resting trials retained the water amount, duration, surroundings and reading procedure, omitting paddle motion to estimate environmental heat exchange. A screen reduced thermal radiation from his body. His calculation included the vessel and paddle heat capacities, external pulley/string losses, descent kinetic energy and string elasticity; it acknowledged residual vibration and sound.^[ref]

The measured observable is a corrected temperature rise, interpreted through the participating heat capacity; it is not a direct view of molecular motion. The experiment tests whether measured mechanical input accounts quantitatively for thermal storage. Frictional warming by itself would establish neither the conversion factor nor the absence of heat exchange. A modern authored demonstration at UCSB instead measures crank turns and a cylinder's temperature with an electrical thermometer: the apparatus differs, but again both mechanical input and thermal response must be measured. ^[ref]