= Heat-engine calorimetry
Heat-engine calorimetry measures <heat> transfers so that observed <work> can be compared with the correct <energy> input. Measuring motion alone cannot supply the denominator of <thermal efficiency>.
The institutional <Laboratory 16: Stirling Engine> describes a modern teaching arrangement: an <ethanol> lamp drives a <Stirling engine> coupled to an electrical output device, which supplies a <resistor> immersed in <water> in a <calorimeter>. The prescribed readouts include fuel <mass> consumed, the <pressure>-<volume (thermodynamics)> loop, electrical readings, and <water> <temperature>. The sequence separates fuel input, gas-cycle <work>, electrical output, and <Joule heating> of the <water>. Warming of the <water> is the final useful output; it is not the engine's rejected $Q_c$. The handout distinguishes warm-up from steady operation and asks students to compare the final warming with direct heating by the lamp. It gives a procedure, not a table of measured efficiencies. Its pp. 1–3 therefore establish an apparatus and measurement design without supplying a new experimental result.
For a proposed calibration, use a known input of electrical <work> to determine the effective <heat capacity> $C_{\rm eff}$ of the <water>, vessel and immersed parts; stir to make the measured <temperature> representative. A matched run with no input estimates exchange with the room. For constant $C_{\rm eff}$ and no <phase transition>, the resulting model is
$$
E_{\rm in}=C_{\rm eff}(T_f-T_i)+Q_{\rm leak,out},
$$
where $Q_{\rm leak,out}$ is the signed net <heat> lost to the room during the measurement. Here $E_{\rm in}$ is supplied electrical <work> when the <resistor> lies inside the calibration boundary; for a separate external <heat> input it is the received <heat>. These are proposed controls, not controls reported in that handout. Slow cooling, changing material properties and imperfectly matched room exchange limit this inference; the approach to <thermal equilibrium> and <heat capacity> matter as much as the thermometer reading.
To measure the actual engine-input $Q_h$, one must instrument its hot-side transfer separately, or close a calibrated <energy> balance around a specified heater boundary. A heater's electrical <work> includes changes in its stored <internal energy> and <heat transfer> that bypasses the engine. At periodic operation a cold-side flowing-<water> measurement can instead estimate $\dot Q_c=\dot m c_p(T_{\rm out}-T_{\rm in})$, if <mass flow rate> $\dot m$ and <specific heat capacity at constant pressure> $c_p$ are known, with negligible storage and other <heat> exchange in that measurement boundary. It measures only the rejection captured by that stream. Include all remaining transfers before using the residual to infer $\dot Q_h=P_{\rm out}+\dot Q_c$. This measurement discipline makes a comparison with <Carnot's theorem> meaningful.
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