Let's say I wish to build an engine which will launch a box vertically upwards. I propose two such engine designs:
Engine 1 (finger, spring, box)
Step 1: Orient uncompressed spring vertically.
Step 2: Place box on spring and use finger to compress spring. Box is now loaded.
Step 3: Remove finger. Spring expands/decompresses. Box is launched by this expansion to some max height.
Overall efficiency: Assuming (nearly) ideal spring, negligible air resistance and frictional heating, then the finger did work W, almost all of which was converted into gravitational potential energy U_g. Seems pretty efficient, in that nearly all work done by the finger was converted into U_g by the engine.
Engine 2 (hot water bath, ice bath, empty 2L bottle, box)
Step 1: Orient empty, capped 2L bottle horizontally.
Step 2: Place box on bottle and place system in ice bath. Thermal energy flows from bottle to ice bath, and bottle partially collapses. Box is now loaded.
Step 3: Remove bottle from ice bath and place in hot water bath. Thermal energy from from hot water bath to bottle, and bottle rapidly expands. Box is launched by this expansion to some max height.
Overall efficiency: Assuming negligible air resistance, then bottle did work W on system, not all of which was converted into gravitational potential energy U_g, since not all thermal energy added to bottle through heating was transformed into U_g. That must be the case, because air in bottle has a measurably higher temperature when the box is at max height than compared to when it was not in either bath. Seems less efficient, in that, not even close to all the work done was transformed by the engine to do what I wanted it to do.
Obviously, engine 2 is an unconventional way to accomplish this task, but it does work (I've done it).
(1) Given that the efficiency of engine 2 is less than the efficiency of engine 1 (a heat engine), why do we primarily use heat engines?
(2) Also, is anything wrong in my analysis/steps above?