 Solution

For direct conversion, descending masses can drive paddles in an insulated vessel of water. Measure the lost gravitational potential energy and the temperature rise, including the vessel's heat capacity and corrections for unwanted heat transfer. Repeated reversal of the paddles and fixed baffles inhibit simple bulk co-rotation, directing more of the input towards dissipative fluid motion. Joule's paddle-wheel experiment tests a quantitative mechanical-to-thermal balance, rather than merely observing that stirring can warm water.^[ref]

For conversion through electricity, mechanical work drives a generator, whose electric current passes through a resistor in a calorimeter. The measured electrical input is $\int VIdt$, or $I^{2}Rt$ for constant electric current and electrical resistance. Joule heating increases the internal energy of the resistor and surrounding water. Compare the generator's mechanical input with the total thermal gains, including generator and circuit losses if the system boundary contains them. A battery alone demonstrates electrical-to-thermal conversion; without accounting for a mechanically driven source it does not establish the requested mechanical intermediate chain.

Using the given value relative to water, the copper requiresWith the modern thermochemical calorie, $1\mathrm{cal}=4.184\mathrm{J}$, so the ideal required work isEquivalently it is about $203\mathrm{kgf}\mathrm{m}$ using standard gravity. A nineteenth-century numerical equivalent of heat could give a slightly different rounded result. The stipulated constant specific heat capacity is used here; an unprovided vessel heat capacity and environmental losses would add to the required input.