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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]

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.^[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.^[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 iswhere $C_{\mathrm{eff}}$ is its participating heat capacity, approximately constant over the run, and $Q_{\mathrm{room}}$ 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.