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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).

Two questions:

(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?

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  • $\begingroup$ Your analysis of engine 1 is incomplete as the finger and the associated biological system are part of the engine, but you have neglected to figuring them in. $\endgroup$ – dmckee --- ex-moderator kitten Jan 12 '19 at 23:56
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Why do we primarily use heat engines?

Before engines were invented, all human work was done using manual labour. The time humans have spent with engines is less than what we have spend without it.

We use them to lessen the work done by humans. Yes engines are less efficient than a purely mechanical thing but what you should also mention is the speed(rpm)of these engines to the work.

Would you cycle your way to a long journey or would you like to take a car?

The car is so to speak more time-efficient for the person than a cycle. So what you should be asking is efficiency of what? Even the human body which is the case 1 is not 100% efficient (as mentioned by David below, we humans are extremely inefficient machines).

So both the cases you mentioned are extremely inefficient methods.

And no, nothing is wrong with your analysis.

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    $\begingroup$ If you look at an exercise physiology book, you will find that human beings operate at a very low efficiency, given that most of the chemical energy of food is turned into heat in order to hold internal temperature at 98.6 deg F. This means that while the spring in Engine 1 (above) has a very high efficiency, the human that compressed the spring does NOT. $\endgroup$ – David White Jan 12 '19 at 19:11
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I don’t think there is anything wrong with your analysis. However, I think your original premise is incorrect. When you say heat engines are so inefficient, I think you are confusing the efficiency of the engine with the efficiency of the thermodynamic cycle in which the engine operates. The efficiency of that cycle is limited by the maximum possible efficiency of the Carnot cycle.

I agree your engine 1 is nearly 100 percent efficient (given no friction, air resistance, ideal spring). But I can give you an example of a heat engine that is also nearly 100 % efficient. Consider the heat engine (piston/cylinder) of a Carnot cycle. During the reversible isothermal expansion, the heat engine converts 100 % of the heat transferred to the gas into work. But in order to return the system to its original state, an isothermal compression rejecting heat is required. As a result, not all of the heat transferred to the system performs work, thus, the cycle is less than 100 % thermally efficient. But there is net work done by the system.

In your engine 1 example, the box initially has no kinetic energy and the spring has potential energy. Upon launch the box leaves the spring with some initial kinetic energy, which equals the loss of the spring’s potential energy. The box reaches some maximum height such that its kinetic energy is zero and its gravitational potential energy equals its initial kinetic energy. But order to “complete the cycle” (return the box to its original state just after launch) the box falls giving up all its gain in potential energy converting it to kinetic energy just prior to impacting the spring. After compressing the spring the box has no kinetic energy and the spring has its original potential energy. The system has returned to its original state. However, the net work done for this “cycle” is zero.

Hope this helps.

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  • $\begingroup$ His engine 1 is decidedly not 100% efficient. He has simple neglected to included the inefficient parts in his analysis. $\endgroup$ – dmckee --- ex-moderator kitten Jan 12 '19 at 23:57
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This is a very interesting thought to think about. But, I do see a flaw in your analysis. There is no escaping heat engines: anything alive is a heat engine.

The spring system is powered by a human, which is a very inefficient heat machine, that is very much so a part of your mechanical engine.

And like @Bod D said, engines are cyclical and must reset to begin again. The agent that resets the spring machine is the human. The heat machine example could be set up with no human required, just a heat source (I'm envisioning something like a lava lamp). It could be made more efficient and more effective than your food powered finger. It would easily be more effective because you would be able to do other things while it was happening and make many more in parallel.

Long story short, fuel is cheap and my time is valuable. In the same vein, you could research what applications are suitable for the Sterling cycle vs the Carnot cycle or the Otto cycle or the Rankine... or Benson-Calvin cycle to get out of the box of human made cycles.

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We use heat engines because they can operate continuously with a thermodynamic cycle (e.g., the Rankine cycle for typical modern power plants), given that they have some sort of heat source (e.g., combustion, nuclear, solar, etc.).

If we continuously generate work in this manner, we can store it (e.g., as electricity on the grid) and then use it for later (e.g., to load the box onto your spring).

The main problem with your analysis and conclusion is that no one uses heat engines to perform tasks like launching an object (except for combustion engines, where the gas expansion work is more than enough to move an object).

We use heat engines because when combined with thermodynamic cycles, we can continuously generate and store energy for later use.

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