Why a temperature differential?

[Jack]

If a fluid is heated it will keep expanding until it reaches ambient temperatures again?

I calculated that theory in the "Let's beat up Carnot" thread. The expansion stops when P inside equals P outside. The temperature ends up hotter than Tc. The extra temperature holds the larger volume. It doesn't go down to Tc until pressure is well below atmospheric. Again that is a manifestation of internal energy. Work out was way less than heat in.

Gas only expands if the chamber gets larger. The enlargement of the chamber can be from internal or external forces, or a battle between the two.

I was leaving out any work or anything other than pure hypotheticals.

Let's say I do expand the fluid until Tc is reached. Do I end up with a bigger volume but lower density? And as I understand you saying now, I'll end up with lower pressure as well?

Edit, I guess lower density means lower pressure. It's a bit of a weird phenomenon though. Something seems to get lost somewhere.

[Jack]

To me this still signifies there's a huge loss in turning heat into pressure through that internal energy.
I'm excited to try my experiments with turning heat into kinetic energy. I'm hopeful that's a lot more efficient.

[Tom Booth]

To me this still signifies there's a huge loss in turning heat into pressure through that internal energy.
I'm excited to try my experiments with turning heat into kinetic energy. I'm hopeful that's a lot more efficient.

Personally Jack, I would not give much, if any weight to "fools" assertions. Unfortunately, in my experience, he likes taking on the role of a knowledgeable infallible expert "teacher" even in areas where he obviously has no idea what he's talking about.

Just for example, I think your own common sense will tell you that this statement is incorrect or at least not necessarily always so:

The expansion stops when P inside equals P outside

I think it is quite obvious that any engine with a piston, connecting rod, flywheel or crankshaft having weight and inertia will continue beyond the point where the internal pressure drops below atmospheric pressure. A lot depends on the weights, how long and how rapidly heat is applied, etc.

Infact, this is what has been observed, measured and recorded on several real time PV data recorders by a number of competent and independent researchers.

Andrew Hall for example, secretary of the European Stirling Engine Society posted this video:

https://youtu.be/SHyke4hUNOs

Which includes these actual PV recordings from his engine:

Compress_20240629_034151_1253.jpg (23.14 KiB) Viewed 4441 times

The horizontal red line indicates atmospheric pressure. The banana shaped curve is the engines internal pressure which as can be clearly seen falls far below atmosphere pressure at BDC.

Some of that may be attributed to the displacer (cooling) but Hall attributes it to the momentum of the piston, which is certainly a factor to consider.

I do not wish to criticize anyone or interfere in other people's conversations, but when there is someone passing quite obviously false, and provably and known false and misleading information, I think I would be remiss not to point that out.

Many people come to this forum looking for accurate and reliable information about Stirling engines. I do not consider my opinions above anyone else's, but these are actual recordings, real data presented by competent recognized experts in the field, not just some anonymous self appointed know-it-all on a message board.

[Jack]

Not to discard or talk over what you just explained, but I'm trying to get to the bottom first. Without engines in mind yet.

What happens to a fluid when heated up and how does manipulating either temperature, volume or pressure change that.

So if you heat a liter of air, expand it until it's back to starting temperature, what do you end up with? Bigger volume, lower density, same pressure?

[VincentG]

Jack if you heat 1 liter of 300k air to 600k and expand it adiabatically, it will reach 1 bar well before it lowers to 300k.

I'll try to find the real values fir you but maybe Matt will beat me to it.

[Tom Booth]

Jack if you heat 1 liter of 300k air to 600k and expand it adiabatically, it will reach 1 bar well before it lowers to 300k.

I'll try to find the real values fir you but maybe Matt will beat me to it.

Just curious, but how do you heat air and have it expand adiabatically?

[Jack]

I assume that's the same for every fluid then?
Of course they'll all have different values.

[Jack]

Jack if you heat 1 liter of 300k air to 600k and expand it adiabatically, it will reach 1 bar well before it lowers to 300k.

I'll try to find the real values fir you but maybe Matt will beat me to it.

Just curious, but how do you heat air and have it expand adiabatically?

First do one, then the other.
This is just to get an understanding of what air or a fluid goes under these conditions.

[VincentG]

Jack I would recommend you do some research on Wikipedia, don't let Tom confuse you over these basic issues. Having alternative views and theories is great but you should first (try to) understand the established theories of thermo.

[Fool]

Jack, that question is answered by the ideal gas and density equations, and adiabatic process.

Density equals mass divided by volume. Volume gets larger. Mass stays the same, no gas leakage.

PV=nRT

And that leads to P1V1/T1=P2V2/T2

I learned those two equations in highschool. I learned how to derive the second from the first, in college.

V1=1
V2=V1=1
V3=?

T1=300
T2=900
T3=T1=300

P1=100
P2=?
P3=?

P2=P1T2/T1=100•900/300=300

The following equation is one I rearranged from Wikipedia:

https://en.m.wikipedia.org/wiki/Adiabatic_process

P3=P2(T3/T2)^(gamma/(gamma-1))

Gamma = 7/5 for diatomic gas such as nitrogen, oxygen, Hydrogen.

P2=300(300/900)^((7/5)/(7/5-1))= 6.415

Very low pressure.

From that we calculate V3:

V3=V2•(P2/P3)•(T3/T2)=1x(300/6.415)x(300/900)= 15.588

V3 is about 15.588 times larger. So density will be 15.588 times lower.

[Fool]

Just as you have been doing to me and others on this forum since your arrival.

It is not I that discourages you. The Carnot theorem is reflecting nature. Nature will discourage anyone by failure. The Carnot rule protects a very long drawn out process of building leading up to what has already learned to be a failure.

Instead it can be used to help. Oh my! My engine is only getting an efficiency of 1.5%! Wow! That's good! What do you mean? Well Carnot says the maximum you will get is 2%. You are getting an incredible 75% of the Carnot limit. That is way better than most engines. Keep up the good work.

[Fool]

To me this still signifies there's a huge loss in turning heat into pressure through that internal energy.
I'm excited to try my experiments with turning heat into kinetic energy. I'm hopeful that's a lot more efficient.

The early steam engines ran on very low temperature differentials and low pressures. They were essentially failures because the amount of fuel needed. The Carnot rule pointed out the efficiency gains at higher temperatures and pressures. It worked and steam boats and trains became viable. This was all because of the Carnot theorem.

If there is 'free' waste heat, it's not the efficiency that will kill the project, it is the cost per kilowatt hour of energy. It requires large machines to extract a little power out of 3 degrees temperature difference. If you can build cheaply it will work. But it will be a large machine.

Holding out for above Carnot claims will just make you go bankrupt waiting.

Tom is a very creative guy and he may one day produce an excellent engine, but it will be consistent with the Carnot Theorem.

[Fool]

The expansion stops when P inside equals P outside.

Jack, Tom likes to cherry pick my errors and write is own twists to them. He is correct that that statement is wrong. I should have written it as:

The effective expansion stops when P inside equals P outside.

Tom posted the following image:

Tom's

Compress_20240629_034151_1253.jpg (23.14 KiB) Viewed 4409 times

Unfortunately it fails to show work input. That is work necessary for pulling a vacuum, and for compression. I've added the areas that add up to 'negative work' to the photo:

The effective expansion is that to the left of the area I put the red squiggly line.

[Jack]

You lost me with the math stuff. I really struggle reading any of that, especially when it's not in it's proper format. Just my math dyslexia.
I guess I was fortunate to be able to avoid it as an engineer. But school was hell because of it haha.

I'm trying to avoid the semi-personal vendetta you guys seem to have haha. Two different views and I'm trying to understand both.

[Tom Booth]

Jack if you heat 1 liter of 300k air to 600k and expand it adiabatically, it will reach 1 bar well before it lowers to 300k.

I'll try to find the real values fir you but maybe Matt will beat me to it.

Just curious, but how do you heat air and have it expand adiabatically?

First do one, then the other.
This is just to get an understanding of what air or a fluid goes under these conditions.

Well, how?

You indicated "Without engines in mind".

To first "heat 1 liter of 300k air to 600k" without the gas expanding would require confinement of some kind.

Following that with adiabatic expansion would require some circumstance or mechanism for removing such confinement. That could be accomplished in various ways.

If not in an engine cylinder than you will, I think, need to clarify what circumstances you have in mind.

What do you mean by "these conditions?"