= Calorimetry
{wiki}
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 $Q_{\rm in}$ be net inward <heat> and $W_{\rm on}$ net inward <work>. The <first law of thermodynamics> gives
$$
\Delta U=Q_{\rm in}+W_{\rm on}.
$$
If 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 (thermodynamics)>, 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>.<Chemistry 2e by Paul Flowers and others/5.2 Calorimetry>[§5.2, paragraph beginning “If the amount of heat absorbed by a calorimeter”, and Figure 5.17: vessel storage, constant-pressure versus constant-volume apparatus and calibration]{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>.<On the Mechanical Equivalent of Heat by James Prescott Joule>[p. 82, Table IX and concluding paragraphs: water-series equivalent and residual losses]{ref}
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