= Mechanical input and thermal storage in a calorimeter
The UCSB demonstration uses an <aluminum> cylinder turned by a crank, with a wrapped rope supporting a hanging <mass>. An embedded electrical <thermometer> connects through sliding contacts to an <electrical resistance> meter; a supplied <electrical resistance>–<temperature> table or fitted equation converts the readout. A counter records turns. Record the initial <temperature>, crank steadily, then stop and convert the minimum recorded <electrical resistance> to the final <temperature>.<UCSB Physics Lecture Demonstrations/52.33 -- Mechanical equivalent of heat>[UCSB Physics Lecture Demonstrations; UCSB demonstration 52.33, opening apparatus paragraphs and “Operating the demonstration”: cylinder, rope, turn counter and resistance calibration]{ref}
The proposed control is to start below room <temperature> and finish comparably above it, approximately balancing incoming and outgoing environmental <heat>. Neglected accessory <heat capacities> and rough <temperature> estimates limit accuracy. The mechanical input and thermal response test an <energy> balance; warming alone does not establish quantitative equivalence.<UCSB Physics Lecture Demonstrations/52.33 -- Mechanical equivalent of heat>[UCSB Physics Lecture Demonstrations; UCSB demonstration 52.33, final operating paragraphs: symmetric temperature preparation, environmental heat exchange and omitted apparatus capacities]{ref}
This is a modern companion to <Joule's paddle-wheel experiment>, with a different apparatus. Choose the cylinder as the <closed system>. When endpoint bulk mechanical <energy> changes are negligible, a model for its thermal storage is
$$
\Delta U\simeq C_{\rm eff}(T_f-T_i)=W_{\rm on}+Q_{\rm room},\qquad W_{\rm by}=-W_{\rm on},
$$
where $C_{\rm eff}$ is its participating <heat capacity>, approximately constant over the run, and $Q_{\rm room}$ is signed environmental <heat>. The cylinder is not an <isolated system>, since mechanical <work> enters. The <temperature> rise estimates a change in <internal energy>, rather than an amount of externally supplied <heat>. This boundary distinction connects a measured thermal response to the same stored quantity used in <two reversible ideal-gas paths between the same states>.
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