Magitech society needs a heat engine

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Magitech society needs a heat engine

Postby jseah » Fri Feb 23, 2018 2:47 pm UTC

So I have a story in which a society new to magical technology is trying to come up with an engine that can efficiently convert magical power into physical motion.

A quirk of the magic system is that directly moving things yields about 100 times less (joule) energy than heat per magic power unit. Thus, a project is born to engineer a heat engine that can efficiently convert heat spells into physical movement.

Heat spells don't have matter, you can target any non-micro size volume you like and dump all your energy into it. On the other hand, this also means that you don't have combustion products to push your engine around.

So the question becomes, what sort of design of heat engine would be good for this? Steam engines could work yes, but what about internal combustion (without the combustion)? Could a piston engine work with air as a working fluid?

Is there a working fluid that would be better than air / steam? What sort of properties would be good to have?
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Re: Magitech society needs a heat engine

Postby eran_rathan » Fri Feb 23, 2018 4:14 pm UTC

You should look into a Stirling Engine for that.
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Re: Magitech society needs a heat engine

Postby Tub » Fri Feb 23, 2018 5:17 pm UTC

A heat engine requires neither combustion nor vaporization. It requires a hot end, a cold end and a working substance in between. Taking any real-world heat engine and replacing coal fire with a magic spell should be straightforward.

Look at engines or power plants developed by humanity when we had the same technological level as your fictional society. Depending on the scarcity of magic energy and other economic factors, your society may have been more or less incentivised to research efficient engines, so adjust accordingly.


You said your kinetic magic has an efficiency of 1%.
Simple steam engines yield <10%, mostly because the temperature difference of your heat engine is low if you exhaust hot steam.
Modern (coal powered) power plants can reach 40-50%.
The theoretical maximum depends on the temperatures of the hot and cold ends of your engine, 60-70% as a ballpark.


All of this can change drastically if you have a cold spell, depending on its cost.

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Re: Magitech society needs a heat engine

Postby jseah » Fri Feb 23, 2018 5:40 pm UTC

Oh yes, there is a cold spell and it's pretty overpowered in thermodynamics terms. Being exactly as efficient as the heat spell.

IE. a cold spell can absorb exactly as much heat energy as the heat spell outputs for the same magical power.

And this doesn't get any harder the lower the temperature of the objects in the affected area. (same for heat spells actually) And yes, this does mean that achieving absolute zero (or something close to it) is actually quite easy, just an application of sufficient power.

I had some ideas on using that, like bringing the existence of air fractionation much earlier than they would normally achieve at their tech level. Meaning that despite being at an early industrial era, upgrading a Bessemer to basic oxygen furnace is actually possible.

How would that affect heat engine designs?

I've known about stirling engines but I don't think we have widespread industrial applications for them? Could one be made efficient with a simple design (ie. no mathematically complex shapes like turbines) and early steel given that heat sinks don't really need to exist?
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Re: Magitech society needs a heat engine

Postby gmalivuk » Fri Feb 23, 2018 5:46 pm UTC

If you can magically add and remove an arbitrary amount of heat, that's effectively infinite free energy right there, which might break whatever society you're trying to build around this magical tech.
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Re: Magitech society needs a heat engine

Postby jseah » Fri Feb 23, 2018 6:20 pm UTC

They're limited by available magical power. It's sort of like a fuel, which yes, does not conserve energy, but nevertheless, they are limited by the total amount of magic their infrastructure can gather and store.
An analogy would be that magic is sort of like solar power. It's more or less just there for the taking, but you got to make enough solar panels to get sufficient power to do what you want and it's not cheap enough to waste.

Storage limitations also mean that magical power is limited in mobile devices like vehicles and areas where you can't plonk down a huge expensive installation (eg. war front). This means that they can't just eat the inefficiency of kinetic vs heat if they say, want to ever build a magic powered airplane.

It's a somewhat different tech base, with magic power behaving like oil in infrastructure terms (collector wells, pipelines, bottled magic) but applications are like electricity (very broad given the correct magical devices).

In any case, optimization for heat engines are still going to be important since converting magic power to physical work is going to be a huge part of what magic is useful for. (the other is of course magic -> heat)


In tech level terms, I'm thinking right around the time when coal and steam just started on Earth. Steel is the new wonder material, production is just starting to ramp up into "can make buildings out of steel" level. Politically, a middle class is appearing, old political and financial systems are showing strain; standardization and interchangeable parts is the new business buzzword that no one is quite clear what exactly it means. Magic is starting to be taught in schools and the total magical power is also increasingly steadily.
Basically, it's right around the time that a new efficient engine for generating physical work to replace human / animal power will become wildly successful and graduate them to a full blown industrial revolution.
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Re: Magitech society needs a heat engine

Postby gmalivuk » Fri Feb 23, 2018 6:53 pm UTC

jseah wrote:
They're limited by available magical power. It's sort of like a fuel, which yes, does not conserve energy, but nevertheless, they are limited by the total amount of magic their infrastructure can gather and store.
You said, "And this doesn't get any harder the lower the temperature of the objects in the affected area. (same for heat spells actually)"

That sounds like you mean the amount of magical energy doesn't change with the temperature, which is infinite free energy.

Did you instead mean that 1 "joule" of magical energy can add or remove one joule of heat energy from a region regardless of the previous amount of energy there, but that you still need to spend 273 times more magic to lower the temperature by 273K than you spend to lower it by 1K?
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Re: Magitech society needs a heat engine

Postby Pfhorrest » Fri Feb 23, 2018 6:55 pm UTC

Here is a thought: how magically difficult is it to move heat, compared to creating or destroying it?

If you can transfer the heat from one volume of working medium to another more efficiently than magically removing the heat from one volume and then magically creating the same amount in the other, then that's a way more efficient way of generating mechanical energy in a heat engine. Just magically move the energy from the cold end of the engine to the hot end and extract the energy as the system returns to equilibrium again, and repeat.

On a further tangent: how difficult would it be, magically, to create and sustain some kind of force field that only lets things pass through one direction, and doesn't produce heat as a byproduct? Such a thing would directly convert heat into kinetic energy if placed inside of ring-shaped tube: the air inside the tube would start flowing one direction and get colder as the random motion of air molecules became uniform motion, and then heat from the environment would rush into the now-colder air, which would then be turned into more uniform motion, and so on. You can then use that air movement to produce any other kind of movement you want, mechanically.
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Re: Magitech society needs a heat engine

Postby jseah » Fri Feb 23, 2018 7:29 pm UTC

gmalivuk:
A piece of matter at 273 K has a certain amount of heat energy. This is basically heat capacity integrated over 0 - 273 K. Another piece of matter at a higher temperature (say 400K) has exactly twice the heat energy of the first.

To cool both to absolute zero would cost exactly double for the second piece. (a bit more / less depending on heat transfer from environment but spherical cow)

IE. if your material requires X joules be added/removed to increase/decrease temperature by 1K, it doesn't matter what temperature the material is. The amount of magic it takes to add/remove that X joules only depends on X.

The exception of course is that at super low temperatures near absolute zero, the spell stops working (no energy to remove) but also doesn't consume power. There might be some weird effects close to it too. Not important.


Pfhorrest:
Heat can't be moved magically. There are magic system reasons why this is the case, based on how magic purely local with no action at a distance. Yes, that means to do anything with magic, your magic actually has to travel there first; and any operation that involves moving something from one place to another requires the magic performing that operation to also move from that place to the other.

In any case, you cannot convert heat to magical power nor does magic have a temperature so there is no heat transfer via magic. You'd have to destroy and recreate the heat.

(getting OT)
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Any sort of force field that relies on exerting forces comes under the "using magic to move things" which is 1% as efficient as heat in terms of energy output. This is also wonky in very high speeds relative to the planet since magic also weighs nothing and is therefore a reactionless drive; but this is not important.

Field of force is a more accurate term than forcefield. Barrier-like magic is just a strong effect compressed into a small thin region. There's no boundaries like how a more... definition based magic system would have.
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Re: Magitech society needs a heat engine

Postby gmalivuk » Fri Feb 23, 2018 10:05 pm UTC

It seems that helium would be a good working fluid because it remains gas to such a low temperature.
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Re: Magitech society needs a heat engine

Postby jseah » Sat Feb 24, 2018 3:45 am UTC

Would magically cooling the heat sink be efficient? If that Carnot equation says that with a particular cooling scheme, you can increase efficiency by 10%, then would a non perfectly efficient heat engine also increase by a proportional amount?

Eg. A given heat engine has a 300 J energy difference between the hot and cold side, Carnot equation says that a reversible heat engine can extract 60% of this energy difference = 180 J of work. A real heat engine might be only 30% efficient = 0.3 * 180 = 54 J.
Now, if we remove another 100 J from the cold side, the energy difference is now 400 J, the Carnot equation will say the reversible heat engine has improved due to a greater temperature difference; let's say a reversible heat engine is now 70% efficient = 280 J. Would the same real heat engine be more or less than 30% efficient = 84 J?

This is important for the final magical power -> kinetic energy efficiency as any reduction in the cold side's temperature is also costing magic.


Helium might be hard to obtain. Would hydrogen work?

What are the properties of a good working fluid for such a heat engine? I suspect not the same as refrigerator fluid?
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Re: Magitech society needs a heat engine

Postby gmalivuk » Sat Feb 24, 2018 2:07 pm UTC

Hydrogen is easier to obtain but has a habit of leaking through pretty much anything.
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Re: Magitech society needs a heat engine

Postby jseah » Sat Feb 24, 2018 2:08 pm UTC

How about N2? Nice and inert for ridiculous temperature differences?
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Re: Magitech society needs a heat engine

Postby Zamfir » Sat Feb 24, 2018 2:27 pm UTC

A big, fundamental problem with 19th century steam engines was pressure. Basically, the atmospheric boiling point of water is too low to create an efficient engine, but reliable high-pressure piping and vessels were really beyond the manufacturing and material knowledge of those days. Not just the early-early days, but the whole steam-engine era through. A modern steam plant runs on ten times the pressure of the final generations of steam locomotives, and almost hundred-fold of the first locomotives.

Your cooling spell would change that, I think. The condensation temperature of oxygen and nitrogen is low enough for high efficiency even at low pressure differences. For all I know, you could build something like a Boulton&Watt atmospheric steam engine, except it runs by condensing air instead of steam. And it would already be rather efficient, perhaps even to the levels of early 20th century engines.

Edit: about working fluids. The main reason to use helium or hydrogen in a Stirling motor, would be to reduce friction losses. Those cases have far higher heat capacities than air, resulting in lower massflows and lower friction losses. Friction losses are a big downside compared to phase-change engines. Either efficiency is low or the design becomes big and expensive. Air-breathing engines (ICE, gas turbine) partially avoid that by leaving the loop open, and partially compensate by avoiding the heat transfer step from source to fluid. Your magic could have that latter effect even in a Stirling engine, that would make them relatively more attractive than in our fireheated world.

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Re: Magitech society needs a heat engine

Postby gmalivuk » Sat Feb 24, 2018 4:27 pm UTC

jseah wrote:How about N2? Nice and inert for ridiculous temperature differences?

Nitrogen boils at 77K, while helium does it at 4.2K. If you're using gas expansion/contraction rather than phase-change, that means you can get much higher efficiency out of helium. (If the hot end is 400K, to pick a random number, the maximum possible efficiency is 99% rather than 81%.)

I suspect most of your advantages over real tech will come from the cooling spell rather than the warming spell. We can make things pretty hot already but the heat sink is almost always just the environmental ambient temperature whereas this would allow us to make it much colder without expending obscene amounts of energy.
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Re: Magitech society needs a heat engine

Postby jseah » Sun Feb 25, 2018 7:44 am UTC

Hm. Is a high heat capacity a good thing?
I thought a lower heat capacity means less energy is required to generate a particular temperature difference?

What other properties would a good working fluid have?
> Chemically (magically) inert would be good
> Production cost?
> Containment problems (eg. why H2 is not a good idea)

Air might be the first generation "easy" engines because you can just take a load of air in whenever you need more. So open cycle becomes easy.


Would it be possible to have it work as a "cold engine", where it is the contraction of air that drives the motion? (with the heat sink replaced with a vent to atmosphere)
EDIT: or perhaps the "hot" cylinder is just the atmosphere heating the cyrogenic air.

Materials might be problem however, since cyro conditions might do horrible things to early steel.
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Re: Magitech society needs a heat engine

Postby Tub » Sun Feb 25, 2018 5:53 pm UTC

jseah wrote:Hm. Is a high heat capacity a good thing?
I thought a lower heat capacity means less energy is required to generate a particular temperature difference?

The carnot efficiency is independent of the working fluid. Lower heat capacity just means that you need a larger volume to transform the same amount of energy.

jseah wrote:> Production cost?

In a closed cycle, that's just a fraction of the total engine cost. Nice to have, but efficiency is more important.

jseah wrote:Would it be possible to have it work as a "cold engine", where it is the contraction of air that drives the motion? (with the heat sink replaced with a vent to atmosphere)
EDIT: or perhaps the "hot" cylinder is just the atmosphere heating the cyrogenic air.

Yes, that can work with the environment as the hot end. But efficiency suffers due to the lower temperature difference. Unless it's expensive to include both the heat and cold spell in the engine, you'd want both.

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Re: Magitech society needs a heat engine

Postby Zamfir » Sun Feb 25, 2018 11:08 pm UTC

Maximum carnot efficiency depends on the ratio of temperatures, not the difference. Going entirely 'cold' can, in principle, give you any kind of efficient you want. Going 'down' to the realm of liquid air is comparable (for carnot efficiency) to going up to 800C or so. That's beyond even modern crazy supercritical steam plants.

Hm. Is a high heat capacity a good thing?

It is once friction becomes a major loss source in the design, like in a gas-phase heat engine. Higher heat capacity means a smaller machine for the same friction losses, and capital cost is usually a big factor.

But 'odd' working fluids are only an option if you can build a nearly perfect closed system. That's not easy! Think about seals and lubrication for axles and cylinders. Or just construction joints without welding, or the effects of thermal expansion on leak-tightness. I doubt that it's an option for the time period you're thinking of. The manufacturing precision isn't there, or the materials. Even modern plants are remarkably leaky, most supposedly 'closed' systems (for whatever purpose) come with extensive make-up systems to keep them filled, and to clean out contaminants that seep in from the outside.

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Re: Magitech society needs a heat engine

Postby jewish_scientist » Tue Feb 27, 2018 1:47 pm UTC

I would make it that magical energy can be turned into thermal energy and vise versa. Heating an object decreases the amount of magical energy stored in an object or person and cooling an object increases the amount of magical energy stored in a object or person. In addition, there is an upper limit on how much magical energy can be stored in an object or person.

In this set up, a magical reservoir and a thermal reservoir in this world would act like how a hot reservoir and cold reservoir do in thermodynamics, except that the upper limit on how much energy the magical reservoir can store is an inherent property of that reservoir and is not dependent of how much thermal energy is in the thermal reservoir.

I would also make it that the material and shape of an object changes how much magical energy can be stored (e.g. a smooth gold pendent = a granite pendent with a symbol carved into it). Similarly, different people have different innate abilities to store magical energy and that mental training can increase any person's ability to store magical energy (e.g. a gifted kid = a trained wizard).
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Re: Magitech society needs a heat engine

Postby gmalivuk » Tue Feb 27, 2018 2:15 pm UTC

Then you can write a story where that's how magic works. Meanwhile, jseah is writing about a type of magic that goes into spells which themselves do the heat transfer thing.
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Re: Magitech society needs a heat engine

Postby jewish_scientist » Tue Feb 27, 2018 2:25 pm UTC

A heat engine is any process that turns thermal energy into work. A spell is any process that turns magical energy into something else.
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Re: Magitech society needs a heat engine

Postby jseah » Tue Feb 27, 2018 3:34 pm UTC

Tub & Zamfir:
Tub wrote:The carnot efficiency is independent of the working fluid. Lower heat capacity just means that you need a larger volume to transform the same amount of energy.

Zamfir wrote:It is once friction becomes a major loss source in the design, like in a gas-phase heat engine. Higher heat capacity means a smaller machine for the same friction losses, and capital cost is usually a big factor.

I'm looking at ideal gas law: PV = nRT
where pressure is proportional to temperature. Shouldn't it be that with a lower heat capacity, it requires less heat to generate the same amount of pressure?

Or is it that a higher heat capacity implies a lesser/greater deviation from ideal gas law?
(A low heat capacity gas might generate less pressure than a given temperature would imply; while a high heat capacity gas would be closer to an ideal gas - ie. higher pressure for the same temperature;
Alternatively, a low heat capacity gas might generate some X% more pressure than a given temperature while a high heat capacity gas would generate even more pressure than expected for the same temperature. )


In any case, Zamfir's point about containing special working fluids is a good one. Perhaps this could be mitigated by having a single cylinder design or by sealing the whole thing in a box containing the working fluid (gotta think about how to get the work out of the box, especially pre-electric).

Still, an early version could be a simpler two cylinder: Atmosphere -> hot cylinder -> cold cylinder -> liquid air
that would either generate liquid air for later uses (eg. an engine in an air fractionation plant) or just dumped into atmosphere.

EDIT: what sort of problems would that face? I can foresee issues with cryogenic conditions, which might need a different steel alloy to compensate for. Water condensation might be an issue as well, requiring the cold cylinder to be stainless to prevent rusting.

jewish_scientist:
In this case, I've already got magic system notes and there's no mechanism to turn heat into magic. There is one to turn work done into magic but that's the opposite of what I'm looking for in this thread - compressing magic generates magical power but requires physical force to be exerted, thereby absorbing work.
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Re: Magitech society needs a heat engine

Postby gmalivuk » Tue Feb 27, 2018 4:49 pm UTC

Apart from the addition of magical spells to create or remove heat, I'm assuming your universe still operates with conservation of energy? (You might even be able to say it conserves all energy, including magical, if the magic used to remove heat energy remains in the world as high-entropy unusable magic).

Thus you can only get as much energy out of a pressurized gas as was in it to begin with. If you put less energy in to raise the pressure of one gas by a certain amount than you'd need for another gas, then the first gas holds less potential energy than the second one.

Edit:
jseah wrote:Or is it that a higher heat capacity implies a lesser/greater deviation from ideal gas law?

For an ideal diatomic gas, the molar heat capacity is 5/2 R (at constant volume). But H2 has 16 times as many moles per unit mass as O2. So even if hydrogen and oxygen were both ideal gases, they'd have equal molar heat capacity but hydrogen would have 16 times more heat capacity by mass.

(Of course, for ideal gases it's the number of moles that corresponds to a given temperature, pressure, and volume, not the number of grams, so working with the same number of liters of each, you'd be back to the equal molar heat capacity.)

Edit2:
Here's a table of constant-volume molar heat capacities. Monatomic ideal gases would be 1.5 in the right column and diatomic ones would be 2.5. He, Ar, H2, N2, and O2 are all pretty close to those values.
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Re: Magitech society needs a heat engine

Postby eran_rathan » Thu Mar 01, 2018 5:08 pm UTC

jseah wrote:Tub & Zamfir:
Tub wrote:The carnot efficiency is independent of the working fluid. Lower heat capacity just means that you need a larger volume to transform the same amount of energy.

Zamfir wrote:It is once friction becomes a major loss source in the design, like in a gas-phase heat engine. Higher heat capacity means a smaller machine for the same friction losses, and capital cost is usually a big factor.

I'm looking at ideal gas law: PV = nRT
where pressure is proportional to temperature. Shouldn't it be that with a lower heat capacity, it requires less heat to generate the same amount of pressure?

Or is it that a higher heat capacity implies a lesser/greater deviation from ideal gas law?
(A low heat capacity gas might generate less pressure than a given temperature would imply; while a high heat capacity gas would be closer to an ideal gas - ie. higher pressure for the same temperature;
Alternatively, a low heat capacity gas might generate some X% more pressure than a given temperature while a high heat capacity gas would generate even more pressure than expected for the same temperature. )


In any case, Zamfir's point about containing special working fluids is a good one. Perhaps this could be mitigated by having a single cylinder design or by sealing the whole thing in a box containing the working fluid (gotta think about how to get the work out of the box, especially pre-electric).

Still, an early version could be a simpler two cylinder: Atmosphere -> hot cylinder -> cold cylinder -> liquid air
that would either generate liquid air for later uses (eg. an engine in an air fractionation plant) or just dumped into atmosphere.

EDIT: what sort of problems would that face? I can foresee issues with cryogenic conditions, which might need a different steel alloy to compensate for. Water condensation might be an issue as well, requiring the cold cylinder to be stainless to prevent rusting.

jewish_scientist:
In this case, I've already got magic system notes and there's no mechanism to turn heat into magic. There is one to turn work done into magic but that's the opposite of what I'm looking for in this thread - compressing magic generates magical power but requires physical force to be exerted, thereby absorbing work.


Brass & bronze are better for cryonic conditions than steel, especially early steels, given that they don't rust & have better material properties, excepting cost and weight. There is also whether or not stainless has been invented yet, plus the difficulty in working the stuff.
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Re: Magitech society needs a heat engine

Postby jseah » Fri Mar 02, 2018 2:39 pm UTC

gmalivuk wrote:Apart from the addition of magical spells to create or remove heat, I'm assuming your universe still operates with conservation of energy? (You might even be able to say it conserves all energy, including magical, if the magic used to remove heat energy remains in the world as high-entropy unusable magic).

Thus you can only get as much energy out of a pressurized gas as was in it to begin with. If you put less energy in to raise the pressure of one gas by a certain amount than you'd need for another gas, then the first gas holds less potential energy than the second one.

Well, the magic itself doesn't conserve energy (one of the attractive forces on magic is not a conservative vector field / attendant process is not time symmetric) but that's also subject to needing to be efficient and limits energy available at any one time to infrastructure and tech level.

EDIT: I haven't decided if the universe (without magic) obeys quantum / relativity yet, but at least newtonian physics, chemistry and even most of biology would apply within their domains.


I understand that energy part, that you can't get more kinetic energy out of an expanding gas than the thermal energy difference. But what I don't understand is that in the ideal gas law, PV = nRT, heat capacity (the part that controls the thermal energy for a given T) does not appear.

Which implies that heat capacity that isn't the same as an ideal gas must indicate a deviation from the ideal gas law equation. I was curious as to which direction the deviation was in (do real gases have lower or higher pressure than indicated for a given volume / temperature?).

I was going to have that appear as a description in the choice of working fluids but it seems that there wouldn't be much difference among the "permanent" gases so air is basically going to be it, which given the temperature difference and tech level would be more or less the only choice.

eran_rathan wrote:Brass & bronze are better for cryonic conditions than steel, especially early steels, given that they don't rust & have better material properties, excepting cost and weight. There is also whether or not stainless has been invented yet, plus the difficulty in working the stuff.

How is brass and bronze better? The civilization does have access to those metals so there's no problem with using it, I'd just like to know what properties makes it better at super low temperatures.


One other issue I just thought of would be that since the output is liquid air, ice is going to be the problem, not water. So rather than dealing with rust, it's more like ice is going to gum up the valves and shaft on the cold cylinder.

They might need a filter on the input to avoid taking in water or run it through a condenser before input into hot cylinder. That said, if you're running a water condenser to 'clean' the input air, a setup involving multiple alternating hot and cold cylinders that feed into the next one down the chain (multiple engines cycling out of phase to provide more constant power) sounds like it could be an obvious 2nd generation engine to save on needing to run more or bigger condensers.


Another is that, looking up the phase diagram of N2, the temperature difference at which it condenses and at which it freezes isn't that large, especially at the <1 atm pressures that would exist during a cold cylinder's power stroke.

While a 10 to 15K temperature difference is a large amount when using our cooling techniques at cryogenic temperatures, this civilization's magic just removes energy directly and the cylinders are already huge considering the ~700 times volume difference between air and liquid air. So somewhat accurate temperature control is going to be needed if they don't want to freeze the liquid air inside the cold cylinder.
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Re: Magitech society needs a heat engine

Postby gmalivuk » Fri Mar 02, 2018 4:31 pm UTC

jseah wrote:But what I don't understand is that in the ideal gas law, PV = nRT, heat capacity (the part that controls the thermal energy for a given T) does not appear.
Why would you expect it to appear directly? Energy isn't one of the terms of that equation, though both sides are in the same units as energy.

An increase of a particular temperature will always correspond to a proportional increase in pressure (for constant volume), but neither side of the ideal gas equation of state tells you how much heat energy needs to be added to get that change. Ideal gases may still have specific heat capacities that change with temperature and/or pressure. For that not to be the case, you'd need a gas that's not only ideal but perfect.
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Re: Magitech society needs a heat engine

Postby Zamfir » Fri Mar 02, 2018 5:45 pm UTC

I understand that energy part, that you can't get more kinetic energy out of an expanding gas than the thermal energy difference. But what I don't understand is that in the ideal gas law, PV = nRT, heat capacity (the part that controls the thermal energy for a given T) does not appear.

Theres two issues here. First, the gas law does not include mass. Try it, divide each side by mass. Density appears on the left, molar mass (m/n) on the right. Gases with a low molar mass have higher specific heat capacities.

Second, and more fundamental, the ideal gas law does not track the internal energy of a gas. Not at all.

Roughly speaking, the stored energy of a gas has two components. The internal energy is the summed kinetic energy of its molecules. That's 3 translational modes per molecule (the temperature), but also all rotational modes, vibrations, etc. Forex, two-atom molecules have roughly 5 degrees to divide their energy over.

The other component is the work-energy, that's the pV of the gas law. This not energy stored in the gas, but the potential energy created by displacing a volume V in the outside world at pressure p. To make room for an extra M3, you have to compress the outside world a little. Or in case of the atmosphere, you lift it a little against gravity.

The gas law is not influenced by the structure of the gas molecules, because it basically tracks the effect of a gas volume on its environment, not the gas itself.

The derivative of the internal energy to temperature is Cv, the specific heat capacity at constant volume. The derivative of enthalpy ( internal plus work energy) is cp, specific heat at constant pressure. Which makes sense, at constant pressure you do work against the environment by changing the volume. R Is their difference, normalized by molar mass

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Re: Magitech society needs a heat engine

Postby jseah » Sat Mar 03, 2018 10:37 pm UTC

Ah, I see. The adiabatic expansion performs work on the piston (integral of pressure over distance moved; which is proportional to volume).

The energy from the work done lowers the temperature of the gas, this is where heat capacity comes in. This lowers the pressure of the gas, thereby reducing work done in the end part of the stroke compared to the beginning as there is less force on the piston.

A lower heat capacity gas would then lose temperature faster and therefore pressure drop is greater and the maximum volume that can be expanded before you reach your final pressure (probably still higher than 1 atm) is lower. Therefore the maximum work that can be done is less for a lower heat capacity gas for a given volume/pressure.
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Re: Magitech society needs a heat engine

Postby Zamfir » Mon Mar 05, 2018 1:31 pm UTC

Yes, that's the basic idea.

I was wondering, how would this question look like to someone who doesn't have our hindsight knowledge of thermodynamic theory? Nor the bag of tricks that we know will eventually be invented to make engines work well?Let's say, the practical and theoretical knowledge of 1700, when the first prototypes for steam engines were built, the Newcomen engine was under development. Except they have these spells.

Just a starting point, I assumed that a spell would act as continuous heat source or sink of (say) 10kW concentrated in a volume of perhaps 10cm radius, could be applied inside a closed volume from the outside, and carried no practical difficulties except that you want to "move" as little Joules as possible. Also, you mentioned an already existing spell that can do work at a "1%" efficiency, so the literal spell-fueled equivalent of a Newcomen engine would not be of much interest. It has to be better than that.

A simple experiment would be to make a closed "Magdeburger sphere", and just keep cooling or heating it. If did my sums right, this should freeze the air in a box even without insulation. Wrap it in some wool, and you can melt any material. At a guess, material development would look very different in such a world, but it is hard to imagine how.

Next step, you notice the higher and lower pressure inside the box, and wonder how to use it. The obvious first step would be to build a hot-air engine, or a cold-air engine. In our world, no one managed to make this work (at any efficiency) until the early to middle nineteenth century. This for example was the best attempt as late as 1807, and it still didn't work.Would the spells change that? In our world, people had to choose between using flue gas directly (which needs an air supply and is therefore difficult keep "sealed" at pressure), or heat from the outside, causing heat-exchanger losses. The spell would solve that.

As a very naive design, let's assume a cylinder with air in it, and a weight on the piston. You heat the gas until it lifts the piston (constant volume heating), then you lift the piston (constant pressure work), the you somehow decouple the weight, push the hot gas out and fresh air in, and start again. Or in reverse, make the weight pull on the piston, and cool the air. I calculate 8% max efficiency (without losses) if you cool down to almost the condensation temperature for air. For heating, you have to heat to 900 C for the same efficiency - not sure if that is practical for an early attempt.

This design would suffer from the Newcomen engine problem - the cylinder is much heavier than the air inside, so you're mostly shoving heat in and out of the walls. At first estimate, this would be bearable because gas-to-solid heat transfer is much slower than transfer by steam condensation, so the losses should be much smaller than in the Newcomen engine. Perhaps this concept could beat the 1% mark already?

Then the next step then seems natural - what if they keep cooling, and condense the air? I have no idea if this could be made to work in practice. The materials, as you say. Not juts strength, but also flexibility of sealing flaps etc. As another example, liquid oxygen is a fire safety nightmare. Perhaps even more for people less used to fire in the first place. There could a be zillion other problems.

If it works, it looks promising. I get to 15% (without losses) on the same assumptions as above - you fill a cylinder with air, condense it while pulling on a steady weight, than let in fresh air in an unpowered expansion stroke. You could even add a separate "condenser", Watt-engine style. A small box with a cold spell concentrated on it, connected at the top to a cylinder which stays at room temperature. This box would suck the main cylinder empty.

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Re: Magitech society needs a heat engine

Postby jseah » Sat Mar 24, 2018 11:12 am UTC

Something like that. I was thinking of having small movement spells (the 1% efficient ones) control valve movements as well, as this makes the valves much easier to build and more robust, due to not needing small mechanical levers.

A second generation engine design I was pondering acts like yours, only there is both heating and cooling spells. The air 'source' is a heated cylinder that pumps air from the atmosphere via a fan or something, heats it up to achieve pressure. The intake valve opens to let the pressurized hot air into the hot cylinder for its power stroke. The cold cylinder's spell turns on at the same time, liquefying the air in that cylinder and drawing the piston down. This liquid air is drained at the bottom of the stroke, just opening the bottom valve and an atmosphere intake to let it flow out.

The engine's flywheel then inputs work to reverse the piston movement. The valves however are only open between the hot and cold cylinder. This moves the hot air to the cold cylinder. The valves close and the cycle completes.

Ideally, you have more than one pair of cylinders running out of sync so as to get more even power as well as run the transfer stroke. Might need a crank start however. =D


I separated the heat input because of the need to have an air input, as well as that coal does exist in this setting so that also allows a non-magical heat input. And if you remember that I had a work done -> magic conversion equipment, the magic cooling of cold cylinder could be powered directly from the steam engine's work if the "boiler" gets its heat from a fuel input. If the engine can be made efficient enough, the load of having to run magic compression for magical power can be less than the by greater extraction of the heat energy content from the fuel.

So it's really a hybrid design.

EDIT: the coal burner might run at ~1000C (copper melting point; achievable since they have steel) and the cold side down to liquefaction (so about -200C). Efficiency between 1300K and 75K is pretty good!
A heat spell can achieve arbitrary temperatures just by adding more power. So a pure magic engine would be able to run at even higher temperature differences than a fuel input. Probably better for applications sensitive to weight and needing high performance, like airship engines.

The reason for that insane hot air input temperature is because the working fluid is air and not water, so no boiling water issues. They could just input the combustion product but that would gum up the works with ash. Easier to just use the exhaust in a reheater for the air intake.

In practice, the working temperatures are going to be much more gentle than the energy inputs could feasibly achieve since the parts aren't going to withstand it.


Further research on the cryogenic issue seems to indicate that if they have decent-ish steel, they could probably get away with just a thicker wall for the cold cylinder. It's the valve sealant that is going to be a problem, since a sealant that might be used in the hot cylinder would probably freeze in the cold cylinder and not work.

I still have no idea how to handle water content in the input air. Having ice in the cold cylinder would be terrible! Maybe recycle the liquid air to use it to condense the water in the air intake?


Some optimizations immediately come to mind, eg. using refractory materials for the hot cylinder so you can go to a higher temperature, vacuum insulation on the cold cylinder, etc. but those are extras.

Hazards too. Like you said, liquid air turns any flammable materials into fire hazards. Wood construction is not recommended nearby. If you're using say coal as a fuel source for the hot cylinder, well... although maybe you could vent the liquid air into your furnace for more complete combustion?


RE spell limitations:
Your interpretation is actually almost correct. Spells don't collide with mundane materials, only with other magic (and enchanted objects, which are just spells anchored to an object; and magical materials). The heat and cold spell act by applying an accelerating force on all molecules within a zone in the same direction as they were already moving; so they output heat energy at pretty high rates.
Spell control also works a lot like mechanical valves, only they aren't material switches so aren't affected by things like heat and cold and chemical attack. Getting hit with a dispel though... no more engine.

In general, a magic engineer has to worry more about how to power the spells rather than how much action the spells can do. If the power can be gotten, using the power isn't too difficult. There are some power density issues at the higher end of the scale but since the current level can compress magic power to output an equivalent amount of heat as burning gasoline in an equal volume comparison, that's good enough for efficient heat engines. (this maximum magic power density achievable is one of the other tech progression indicators I'm using to ballpark what the setting looks like as it improves its magitech)
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Re: Magitech society needs a heat engine

Postby Zamfir » Sat Mar 24, 2018 6:48 pm UTC

I can't quite work out your proposed design, perhaps you can draw it?

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Re: Magitech society needs a heat engine

Postby Eebster the Great » Sun Mar 25, 2018 9:05 am UTC

Is there any real necessity for a cold spell, given you can generate heat? Like, you could always just build a refrigerator. Your whole society could be powered by magic, and all manual labor positions would be this kind of thing.

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Re: Magitech society needs a heat engine

Postby gmalivuk » Sun Mar 25, 2018 2:30 pm UTC

Someone might eventually invent a refrigerator, but but it's a lot more complex than simply applying a cold spell to food. Unless you're suggesting a change to the underlying worldbuilding.
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Re: Magitech society needs a heat engine

Postby Eebster the Great » Mon Mar 26, 2018 2:34 am UTC

But the technology seems adequate, it should develop quickly with so much energy, and as jseah said, "In general, a magic engineer has to worry more about how to power the spells rather than how much action the spells can do. If the power can be gotten, using the power isn't too difficult."

But if efficiency is important and cold spells are nore efficient, then sure. The same applies to anything else magic can do I guess.

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Re: Magitech society needs a heat engine

Postby SuicideJunkie » Mon Mar 26, 2018 6:21 pm UTC

Eebster the Great wrote:But the technology seems adequate, it should develop quickly with so much energy, and as jseah said, "In general, a magic engineer has to worry more about how to power the spells rather than how much action the spells can do. If the power can be gotten, using the power isn't too difficult."

But if efficiency is important and cold spells are more efficient, then sure. The same applies to anything else magic can do I guess.
As I read it, there is just one temperature spell that costs the same regardless of which direction, and going down is thus better.

If the engine is generating liquid air as exhaust, an airship could use it to make a smokescreen of fog and/or induce a but of rain when flying over farmlands and reservoirs. Contrails would be thick in the skies.

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Re: Magitech society needs a heat engine

Postby jseah » Tue Mar 27, 2018 5:56 am UTC

Zamfir wrote:I can't quite work out your proposed design, perhaps you can draw it?

Spoiler:
Image

Note that the return stroke "costs" power (moving air doesn't take much, but friction counts during a stroke that doesn't do work).

The high pressure hot air intake could be from a separate heat spell setup or a fuel burner. This would also require a separate air intake compressor piston for better efficiency.

In a fuel burner, said compressor would double as a small magic compression engine (convert work to magic power) in order to power to cold spell.


Eebster the Great wrote:Is there any real necessity for a cold spell, given you can generate heat? Like, you could always just build a refrigerator. Your whole society could be powered by magic, and all manual labor positions would be this kind of thing.

Refrigerators would be inefficient unless well insulated. The heat/cold spell might be magically efficient compared to movement spells but it's not that efficient relative to human power.

For comparison, the setting's magically strongest character (who spent nearly all 19 years of her life training specifically for high power and nothing much else) would be able to bring ~300ml of water from 25C to 100C (but not actually boil it!). And then run out of power for the rest of the day. Well, okay, water is a very bad example since H2O's insane heat capacity laughs at your pitiful energy input.

The setting's industrial revolution is getting powered by an invention of magical powerplants that rather similar to oil wells, the first version of which outputs as much power as that character per minute. (and they can be built most places you can dig a deep hole)
So while they do have a decent magical power income and will be using it for everything and anything as that income increases, they do have to watch their efficiency.

Furthermore, as powerplants are a deep hole in the ground (and some stuff), they're not exactly mobile. So if you ever want to get a magically powered vehicle that brings its own stored magical power along, you have to also watch your storage density vs consumption.
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Re: Magitech society needs a heat engine

Postby Eebster the Great » Tue Mar 27, 2018 10:50 am UTC

If magic costs magical energy to use, of which there is a limited quantity that is expensive to produce, and it can only be put to practical use by specific implementation requiring both expertise and technology, it sounds a lot like electricity.

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Re: Magitech society needs a heat engine

Postby jseah » Thu Mar 29, 2018 7:17 am UTC

Eebster the Great wrote:If magic costs magical energy to use, of which there is a limited quantity that is expensive to produce, and it can only be put to practical use by specific implementation requiring both expertise and technology, it sounds a lot like electricity.

All of this is true. Magic is a lot like electricity in the range of applications, need for expertise to build items that laymen can use, benefiting from large scale infrastructure...

With the caveat that magical power infrastructure works more like gas pipelines than electric lines, and power plants are more akin to oil wells than coal burners. But yes, the similarities are there.
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Re: Magitech society needs a heat engine

Postby Eebster the Great » Thu Mar 29, 2018 4:30 pm UTC

Got it, hence the industrial revolution and stuff. Are there complex spells that can do highly specific things?

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Re: Magitech society needs a heat engine

Postby jseah » Thu Mar 29, 2018 5:48 pm UTC

Eebster the Great wrote:Got it, hence the industrial revolution and stuff. Are there complex spells that can do highly specific things?

Unfortunately, all complexity has to be human created. Basic magic is nothing more than defining a volume, picking some effect and going with it.
(currently, the only effects are magic disruption, heat, cool, accelerate, decelerate, deflect, increase inertia)

But...
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One of the most important laws is "there is no action at a distance". Your magic has to go somewhere to have an effect there.

Another one is that "magic does only what you make it do". If you need the effect to turn left, then you either make it a natural result of the spell's operation or you have to cast a spell that turns left. To say nothing of things other settings take for granted like "recognizing objects" or "people".

There's also a branch of effects that converts magical power into magical materials which have their own effects but generally behave like physical materials with strange properties.

And there's a basic toolbox of metamagic, involving sensors (temperature, forces, density, etc.) and a basic spell activation conductor (which can be used to create timers, trigger dormant effects, create logic, etc.).
> There's an issue here where every caster would do things slightly differently even if they used the same spell design. It's like trying to build a clock by hand, down to cutting all the gears with a scalpel and no ruler. Humans just aren't good enough to make things like timers that are reliable beyond a hundred ticks or so. (and trying to standardize the length of a 'tick' between casters is like trying to get people to count to a hundred seconds to themselves. Everyone reaches a hundred at a different time)
> What happens is that every caster develops casting habits tailored to themselves. They know from experience that if they make a timer of this size count to 113 ticks, it will run for about ten seconds (example), and practice it until they can make it accurate to half a second every time.
> Note that spells also suffer wear and tear, parts of them will break over time or drift out of position. The higher the magical energy applied, the faster this happens, the bigger the "parts" of the spell, the more resistant it is (but also more limited in how well it can target things), although a caster can dedicate some amount of magical energy to the spell's structure to make it more robust instead of doing useful things with that energy.

The basic bolt spell has an effect that is triggerable, a sensor for some criteria that triggers the effect, and a push. Eg. the 'standard' firebolt is a create magical material (fire) effect, a sensor for matter density greater than water, and fired at the maximum standard magic conduction rate (about 10 m/s)
Magic disruption is special since it's less an effect and more the result of a dense formation of magic impacting on a spell like a cannonball, so you can just throw it out without a sensor.

Notably, this makes any sort of complexity very difficult before the process can be abstracted and standardized. Around the start of the story, one of the main characters was considered an alchemy genius for having invented the magical arrow.
> Enchanting an arrow to accelerate after firing, while also not being susceptible to things like the sensor in the base accidentally going off when you fall down, is surprisingly difficult; the solution was to have a two-stage activation, the notch in the bowstring was also enchanted to prime the nocked arrows so that an applied force triggers the enchantment to accelerate the arrow after a tiny delay; she received the alchemy genius recognition for the concept of priming.


So there is no such thing as a "door unlocking spell" ala Harry Potter alohomora.
You could get a magical engineer to design and enchant an unlocking spell that would work on a specific design of door, but something as simple as moving the lock mechanisms would make it no longer work.

Of course, if you get really advanced, you could build a system that would search for a lock mechanism of a particular type, identify which parts to turn to draw the bolt. Though that would take a spell that was a generalized computer, a sensor suite sufficient to scan the door, and lots of programming. Definitely not possible at their current tech level.

Things of that level of complexity like summoning stones (hologram projector, simulates physical object by shaping forces or effects, provides command and control for the whole thing so the user only needs to input commands), demihuman races (supersoldier genetic engineering), Dust (magic powered grey goo) etc.
Those things are all lostech.

Yes, I rate a "general door opening spell" to be of the same level as the "Ancient Magical Era"s superweapons.


Currently, the most complex thing they have is a "spellforming wand with slots" which is a tool that can perform the process of casting a spell by mimicking the same steps casters use. This allows a non-caster to connect a power source (which is also another tool that needed designing) and a set of instructions (a step by step list ala CNC instructions) to control the spellforming wand; the combination can then create and cast whatever spell the instructions encode.

This is a lot like a CNC machine in many ways. If CNC machines could create functional objects.

The spellforming wand, and it's magic item creating cousin, the magic circle; these two are also one of the three pillars of the magitech industrial revolution. The other two are the non-human magic energy source and non-human magic storage.
> This is the current 3rd generation of this device in my story. The 1st prototype was a knitting board-like device where you literally had to draw the spell by placing enchanted threads or pins in the correct positions and it would get transcribed exactly in the output; that could only do spells that were flat 2D.
> Also the magic circle (magic item creator) came first, spellforming wand was later. Since standalone spells were extremely time limited, complexity is less rewarded there, while magic items inherently need complexity because they all have dormant and active states and need to know when to switch. So even though the magic circle was more complicated, it was needed first so it got invented first and the principles later applied to the easier problem.

By standardizing casting and enchanting, they make possible the discipline of magical engineering. Where you only have to worry about how to get the spell to do what you want it to, rather than worry about practicing the casting process until you can do it reliably. Plus people don't even have to train to cast spells anymore, you can get by just training how to design spells and have spellforming wands do it for you, faster and better than if you learnt to cast yourself.
(and thus the advent of magical design bugs; which replaced spellcasting failure as the primary reason for spells not doing what you want)

Furthermore, since the process only requires humans to ensure it is running properly, it's also production line friendly. Really, it can do a lot of things, since spellforming wands are essentially 1 abstraction level away from the actual casting of spells.

Of course, the first thing they do is make a weapon model able to shoot fire/force/disruption bolts only (the basic three magical combat spells) and start mass producing it. Suddenly every random guy on the street can be shoved in a uniform, given a magic gun and told "this end towards enemy,
fire when I say so".
> Pre-spellforming version was a crossbow set to launch arrows loaded into it; except that magical shields can usually defeat any one of the possible attack methods and are cheaper than the attack, so you need to have some variety.

I actually put more thought into the magic system design than the story design... which is probably not a good thing.

Then again, I've had this system for years, and spent a lot of the time crafting it so that every step of the way to magitech was fully explained within the system's rules. It was very much a system crafted so that magitech was possible and that I could write about the development.

In other ways, it was also a reaction to what I saw as "magic systems that do things for you". Many magic systems have spells contain ridiculous complexity and when you poke at the seams, all sorts of strange conclusions fall out.
I wanted to avoid that and I think the result is a magic system that is more robust than standard.
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