= Direct calorimetry
{title2=$\dot Q\simeq\dot m c_p(T_{\mathrm{out}}-T_{\mathrm{in}})$}
<Direct calorimetry> measures a process's thermal output or absorption through the response of a <calorimeter>. The observations can be a receiver's <temperature> change or a measured <heat transfer> rate across a controlled boundary. Converting those observations into <energy> or <power> requires a calibrated thermal response and an accounting of storage and losses.
A <flow calorimeter> provides a concrete physical arrangement. A heated component transfers energy to a coolant stream; inlet and outlet thermometers measure its <temperature> rise, while a flow measurement supplies the <mass flow rate>. With negligible changes in bulk <kinetic energy> and height, the stream's enthalpy gain is
$$
P_{\mathrm{stream}}=\dot m(h_{\mathrm{out}}-h_{\mathrm{in}})
\simeq\dot m c_p(T_{\mathrm{out}}-T_{\mathrm{in}}).
$$
Here $c_p$ is <specific heat capacity> at the relevant pressure and temperature. Manufacturer documentation for a water calorimeter likewise describes monitoring water flow and temperature to determine absorbed incident power.<Water calorimeter power detectors by Gentec-EO>[Publisher description, water-flow and temperature monitoring for calorimetric power measurement]{ref}
For an illustrative <water> flow of $0.010\,\mathrm{kg\,s^{-1}}$, a $0.50\,\mathrm K$ rise and approximately $c_p=4180\,\mathrm{J\,kg^{-1}\,K^{-1}}$,
$$
P_{\mathrm{stream}}\simeq20.9\,\mathrm W.
$$
Over 60 seconds at those conditions, the stream carries away about $1254\,\mathrm J$. These assumed values describe a calculation, not a product specification.
A broader energy balance can read
$$
P_{\mathrm{source}}=P_{\mathrm{stream}}+\frac{dU_{\mathrm{stored}}}{dt}+P_{\mathrm{loss}}.
$$
If the vessel is still warming, some input is stored rather than carried away. Heat leakage can also leave the chosen boundary through another path. <Electrical calorimetry> can check the response by supplying a measured heater input and comparing it with the readout. Establishing a steady state, matched thermometer calibration and a clear <thermodynamic system> boundary makes the inferred source power credible.
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