Struggling With Internal Energy..

[VincentG]

Yes, increasing pressure can increase the internal energy of a gas, especially when the volume remains constant. When pressure increases, gas molecules collide more often, which increases their kinetic energy and the gas's internal energy. This is called pressure–volume work, which occurs when a fluid's volume changes while the external pressure remains constant. For example, if a gas is compressed at a constant volume, work is done on the gas, which increases its internal energy. 

This is an ai overview. It seems that for real gasses pressure does infact increase internal energy, but not for ideal gasses, further complicating any subsequent discussion.

PV=nRT is close enough for real amd ideal gasses but maybe any discussion of internal energy with ideal gasses is doomed to waste our own internal energy.

[Tom Booth]

Yes, increasing pressure can increase the internal energy of a gas, especially when the volume remains constant. When pressure increases, gas molecules collide more often, which increases their kinetic energy and the gas's internal energy. This is called pressure–volume work, which occurs when a fluid's volume changes while the external pressure remains constant. For example, if a gas is compressed at a constant volume, work is done on the gas, which increases its internal energy. 

This is an ai overview. It seems that for real gasses pressure does infact increase internal energy, but not for ideal gasses, further complicating any subsequent discussion.

PV=nRT is close enough for real amd ideal gasses but maybe any discussion of internal energy with ideal gasses is doomed to waste our own internal energy.

You need to be a little careful with ai responses.

For example: "Yes, increasing pressure can increase the internal energy of a gas, especially when the volume remains constant."

That makes no sense.

At least not for a Stirling engine. Same problem I was trying to get across with some calculators.

It "assumes" if pressure increases you must be adding additional mass (moles).

Otherwise pressure could be increased (at constant volume) by adding heat.

How can you increase pressure by adding work at constant volume? Not with a piston in an engine.

There is also a chance it is simply quoting or paraphrasing some numbskull on Quora or who knows where, or out of context.

Check the original sources.

Internal energy for a gas, is like pennies in a suitcase. A matter of mathematics.

It doesn't matter how big the suitcase is, just how many pennies go into it. Or get taken out. The empty space in the suitcase is not reckoned in the accounting.

Work or heat can add or take away "pennies".

Additional space, (a bigger suitcase) cannot.

[VincentG]

How can you increase pressure by adding work at constant volume? Not with a piston in an engine.

By adding heat energy at constant volume.

[Tom Booth]

How can you increase pressure by adding work at constant volume? Not with a piston in an engine.

By adding heat energy at constant volume.

Yes, I said that.

I don't know precisely what question you asked the ai, but I would assume it had to do with the subject that has been under discussion here. Jacks question about adiabatic(?) expansion.( I think?)

The ai did not say anything about adding heat.

At any rate, my point was mainly these ai responses are not something I'd draw any hard or final conclusions from, such as: "any discussion of internal energy with ideal gasses is doomed".

Though I've been saying for a long time that "ideal gas law" is limited to a fairly narrow range of gas behavior under "normal" conditions of temperature and pressure.

Start getting into rapid changes, high pressure, or low temperatures and the deviations increase, especially near phase change conditions.

I wouldn't start redefining common thermodynamic terminology like "free expansion" that already has an accepted textbook meaning I think that would only cause more confusion.

I think probably 90% of thermodynamics terminology developed to describe steam engines. IMO, much of it does not apply to Stirling engines. Kind of like trying to fit square pegs into round holes.

Coining some new terms to describe gas behavior in Stirling engines specifically might be in order, but I'd avoid trying to reuse or redefine existing terms.

[Tom Booth]

Let me try putting this another way.

Because so much of thermodynamics developed from and applied to steam engines. Some calculators and such "assume" if you increase pressure you are adding steam.

In a steam engine heat is accompanied by mass. Steam is heat and mass.

I've tried using all kinds of online calculators and found that they do not hold moles constant. I guess because programers are lazy and don't necessarily know physics. The things calculate for the most common use case; steam.

Stirling engines are kind of a special case in that respect, so you need a calculator that does not assume too much.

If it doesn't include moles, it's probably assuming too much.

[VincentG]

I was googling "does internal energy go up with pressure?". I wasn't trying to prove any point in doing so, just see what others had to say.
As I said earlier in this thread, I do struggle with understanding internal energy.

[Tom Booth]

Well, what I do know is that gas liquefaction expanding a gas through a turbine apparently works. Since it is actually used industrially.

Experimentally, allowing a gas to expand into a vacuum does little if anything to reduce the temperature. It might even increase the temperature with certain gases under certain conditions.

The expansion turbine or piston engine works on the principle that "the internal energy of an ideal gas is a function of temperature only"

So by taking out additional internal energy making the gas do work as it expands into a vacuum instead of just expanding into a vacuum (without doing work), reducing the internal energy that way results in a dramatic reduction in temperature.

So, that basically, I would say, pretty .much applies to real gases as well, since it is real gases that are actually being liquified.

At any rate it's a general rule of thumb and, joules experiments were with real gases.

So basically, if no work is done and no heat is exchanged, changes in volume and pressure don't effect internal energy.(Much, usually).

Though I'm at a loss to imagine how a gas could be compressed or the pressure increased without putting heat and/or work into it.

I was reading an interesting discussion on this topic.

If you expand a gas into a vacuum and the temperature remains the same. If you then compress the gas, the temperature increases?

Well, expanding into a vacuum the gas doesn't do any work, but with compression, work is done on the gas, so, I guess so.

[Jack]

If I get this right, you're saying that a hot gas doing expansion work on a piston will cool down more than a (same temperature) gas that is allowed to expand the same amount freely?

Edit: yeah my sleepy eyes didn't read it well, there was no need for my question as it's pretty clear.

[Jack]

If you expand a gas into a vacuum and the temperature remains the same. If you then compress the gas, the temperature increases?

Well, expanding into a vacuum the gas doesn't do any work, but with compression, work is done on the gas, so, I guess so.

This touches on my idea for an engine. What if, while you're expanding gas in a vacuum, it's running through a turbine, doing work. Would that cool it down in your view?

I imagine that might depend on the design. And maybe only because it's giving off heat to the turbine?

[matt brown]

I was googling "does internal energy go up with pressure?". I wasn't trying to prove any point in doing so, just see what others had to say.
As I said earlier in this thread, I do struggle with understanding internal energy.

I tend to divide the most common thermo values into 2 distinct camps (1) UTQ (2) PVW. When J (or similar) defines Q and W then this alphabet soup allows an engine design where Q vs W typically leads the order of merit. Dwelling on any one value is ripe with rabbit holes, since they're inter-related, but most can be related as various ratios (some obvious, some obscure).

Internal energy is the most esoteric thermo value, moreso than entropy which is a bogus statistical derivative (contrived quantitative value of qualitative origin). The problem with internal energy is that it's a "micro state" vs work is a "macro state" and I'm not gonna worry about micro states as long as those gremlins keep winding their rubber bands or whatever they do. However, on the macro side, equating U via J will remain a major challenge since each thermo process (and gas class) has a different relationship. My cheatsheet internal energy value I use is U=15J per 100cc when 300k and 1 bar air which is sweet for isochoric and isothermal processes, but this needs a major mod when isobaric and/or monatomic.

I wouldn't worry about moles unless you want blisters on your fingers from endless calcs. No need for wacka-moles when using J for UQ and W.

[matt brown]

If you expand a gas into a vacuum and the temperature remains the same. If you then compress the gas, the temperature increases?

Well, expanding into a vacuum the gas doesn't do any work, but with compression, work is done on the gas, so, I guess so.

This touches on my idea for an engine. What if, while you're expanding gas in a vacuum, it's running through a turbine, doing work. Would that cool it down in your view?

I imagine that might depend on the design. And maybe only because it's giving off heat to the turbine?

Yes Jack, gas will cool down greatly. The problem is how do you maintain the vacuum ??? which will quickly 'fill up'.

This is effectively what James Watt did...exhausting steam to relative condenser vacuum vs ambient, whereby he gained a lot of extra power for 'free'.

[Jack]

That is the challenge indeed, I'm working on a design that might do that.
But this is kind of unexpected for me, as I would've thought that the friction would actually increase the internal energy.

[matt brown]

That is the challenge indeed, I'm working on a design that might do that.
But this is kind of unexpected for me, as I would've thought that the friction would actually increase the internal energy.

The heat increase from friction will be very minor vs the massive cooling from expansive work.

This idea is far different than cyro cooling where low temperature of reefer has little expansive work occur vs the higher temperature of 'similar' engine.

[MikeB]

If I get this right, you're saying that a hot gas doing expansion work on a piston will cool down more than a (same temperature) gas that is allowed to expand the same amount freely?

I think we are all agreed that this is true.

The issue with a real Stirling (and other engines) is that the reverse is also true - when the piston returns, it does work 'in reverse' thus warming up the working fluid by a certain amount. There will only be a difference if the _engine_ does some work - if we are looking at a 'perfect' engine on paper, with no friction and no load, then the energy lost to the piston on expansion will be cancelled out by the energy gained on compression. (As I understand it.)

[Tom Booth]

If I get this right, you're saying that a hot gas doing expansion work on a piston will cool down more than a (same temperature) gas that is allowed to expand the same amount freely?

I think we are all agreed that this is true.

The issue with a real Stirling (and other engines)...

I think it is a mistake to lump Stirling engines in with "other engines".

All other engines increase pressure by cramming additional mass into the cylinder to carry in the heat as steam or in chemical form for combustion. It is this Mass (moles) that has to be exhausted.

Then more heat can only be drawn in along with more mass. Steam/chemicals.

Stirling engines take in only heat/energy.


So, I think this is probably also bad advice:

I wouldn't worry about moles unless you want blisters on your fingers from endless calcs...

You can't really just use the same equations/calculators, designed for "other engines". I'm afraid.

I had this issue while trying to calculate this PV graph

Resize_20230522_031849_9086.jpg (175.66 KiB) Viewed 3053 times

Many of the calculators gave weird impossible results. I had to find one where I could enter the moles manually. Yes, very time consuming.

Still not accurate though, it doesn't account for changes in velocity.