# Making energy out of freezing ice

Just a thought from a dream Since water expands so greatly when frozen could it be possible to freeze the water in a metal cylinder but one side is like a car piston with a very high gear ratio which would be no problem to turn because the pressure the ice builds up which generates electricity to freeze the water again and repeat (Would doing this test in a vacuum help or?) Please someone debunk me

• It requires energy to freeze something, and the energy required to run the freezer will be much much larger than the work done by the expanding ice cube. Commented May 5, 2023 at 22:40
• @march You are of course right but I expect that the bigger problem will be the realization that the books claiming that "in an isothermal expansion of an ideal gas the absorbed heat is completely converted to work" and similar statements will have to be rewritten. As Truesdell said it "The tragicomedy of thermodynamics has been the persisting tendency to entangle in special constitutive relations, so that the purely energetic content of the theory becomes invisible." Commented May 5, 2023 at 22:55
• @hyportnex The magic of thermodynamics lies in the very fact that it makes miraculously general statements about non-existing systems that are still good to within 5 or 10% in real systems... which has allowed our engineers to build extremely useful steam and internal combustion engines for the last 200+ years or so. I would allow for a bit of imprecision here, especially since all of physics is the art of approximation, after all. Commented May 8, 2023 at 7:04

Since water expands so greatly when frozen could it be possible to freeze the water in a metal cylinder but one side is like a car piston with a very high gear ratio which would be no problem to turn because the pressure the ice builds up

Yes; this is no problem. In fact, if you have an area slightly cooler than the freezing temperature under the high pressure applied by the piston and gears (which will be <0°C) and an area slightly warmer than the melting temperature under atmospheric pressure (0°C), then you can move the device between the two areas, collecting work during the freezing step and allowing the system to reset during the melting step. This is a version of a heat engine.

which generates electricity to freeze the water again

No, you won't generate enough energy to do this. The First Law tells us that you can't extract net work and expect to repeat the cycle in a single location, and the Second Law tells us that you can't even extract that much work, the Carnot efficiency (<100%) being the maximum efficiency obtainable from a heat engine.

(Would doing this test in a vacuum help or?)

Well, the vapor pressure of the evaporating condensed phase (solid or liquid) could be used to produce work—until that phase has evaporated away and the remaining gas has expanded to extreme rarefication. The First Law still precludes you from returning the system to its original state while also extracting net work. The Second Law actually requires you to contribute some additional work to reset the system due to real-life inefficiencies.

• In my upper-division thermodynamics class, I often assign an exercise in which students (a) use the Clausius-Clapeyron law to show that there's a maximum force this engine can exert for a given "cold reservoir" temperature, (b) calculate the work done by this engine given the expansion of water when it freezes, and (c) show that the efficiency of this engine is less than the Carnot limit for the given temperatures. Commented May 8, 2023 at 12:31

Historically, your question is very interesting. The idea that it would seem possible to use this phenomenon to produce work was discussed by William Thomson (the future Lord Kelvin) and his brother James Thomson. In the works of William Thomson , p 196, you find the following quotation:

Article of James Thomson about congelation and liquefaction , 1850

Some time ago my brother, Professor William Thomson, pointed out to me a curious conclusion to which he had been led, by reasoning on principles similar to those developed by Carnot, with reference to the motive power of heat. It was, that water at the freezing point may be converted into ice by a processs solely mechanical, and yet without the final expenditure of any mechanical work. This at first appeared to me to involve an impossibility, because water expands while freezing; and therefore it seemed to follow, that if a quantity of it were merely enclosed in a vessel with a moveable piston and frozen, the motion of the piston, consequent on the expansion, being resisted by pressure, mechanical work would be given out without any corresponding expenditure ; or, in other words, a perpetual source of mechanical work, commonly called a perpetual motion, would be possible.

James Thomson's conclusion was that, to avoid this contradiction, the freezing temperature of water had to decrease when the pressure increases. This last point was therefore found by theoretical arguments before being verified experimentally.

At the time, the link between the specific volumes of the two phases and the slope of the curve $$P(T)$$ (Clapeyron's relation) was not yet known!

I let you read the articles in the same reference if you are interested.

Hope it can help and sorry for my poor english.