Exploring Carnot's and Jordan's Contribution to the Theory of Work

[stevmg]

This chain was "lost" in a previous thread and disappeared into the ionosphere.
The question was based on the principle expounded in 1828 by Sadi Carnot (1796 - 1832) - some French military physicist and engineer - died kind of young.). I never knew the man.

W = efficiency as a fraction of 1.00, T2 = higher temperature Kelvin, T1 = lower temperature Kelvin, Q2 = higher energy level (ratio measurement meaning there is a real "0"), Q1 = lower energy level

W = (T₂ - T₁)/T₂ or, using other energy level units:

W = (Q₂ - Q₁)/Q₂

Now, it has been stated that there is an energy density in the universe...

1) If the universe is expanding, is the energy density dropping and are we, in effect, bleeding off our potential energy for accomplishing work

2) If all the energy is at one energy level, even though not at zero (0), no work can be generated because the numerator in either equation above is zero (T₂ - T₁ = 0, Q₂ - Q₁ = 0), no matter how high T₂ or Q₂ are.

Is this really true? Was Sadi Carnot a really brilliant guy, or, was he "blowing smoke" at us? What are the implications of this?

If we can get solid answers to this I can tell you about a mathematician named Camille Jordan (1838 - 1922), another French guy who did "blow smoke" but the assertion is true. I didn't know this fellow either but I sure would have liked his sales pitch.

 

[bcrowell]

1) If the universe is expanding, is the energy density dropping and are we, in effect, bleeding off our potential energy for accomplishing work

The energy density of the universe is certainly dropping (on the average). For instance, the average density of heat and radiation is decreasing.

Potential energy isn't a very well defined or useful concept in GR. There is no global law of conservation of energy in GR. That makes it hard for me to figure out what kind of work you're referring to here.

2) If all the energy is at one energy level, even though not at zero (0), no work can be generated because the numerator in either equation above is zero (T₂ - T₁ = 0, Q₂ - Q₁ = 0), no matter how high T₂ or Q₂ are.

This isn't a relativity question. If the universe was in thermal equilibrium, then your argument would be correct, and there would be no way to do mechanical work.

 

[stevmg]

The energy density of the universe is certainly dropping (on the average). For instance, the average density of heat and radiation is decreasing.

Potential energy isn't a very well defined or useful concept in GR. There is no global law of conservation of energy in GR. That makes it hard for me to figure out what kind of work you're referring to here.



This isn't a relativity question. If the universe was in thermal equilibrium, then your argument would be correct, and there would be no way to do mechanical work.

You have answered two questions to which, prior to now, I had no clue:

1) I did not know that in GR/SR there was no principle of energy conservation. Now I do.

2) Yes, Messr Carnot was dealing with 19th Century thermodynamics and you validated my understanding of that and, by inference from the answer to question 1, you have indicated that the Carnot Principle would not apply to our Universe "out there." I guess we will have to retire it to steam locomotives and the like.

That was the whole purpose of my questions and you have answered them.

Much thanks,

stevmg

 

[Andy Resnick]

by inference from the answer to question 1, you have indicated that the Carnot Principle would not apply to our Universe "out there."

stevmg

I don't follow your logic, can you please explain? Carnot's principle, which leads to the definition of entropy, does indeed apply to the entire universe and does not require equilibrium.

Edit: this thread may be more appropriate in Classical Physics. Or not, depending on the response...

 

[bcrowell]

[...] by inference from the answer to question 1, you have indicated that the Carnot Principle would not apply to our Universe "out there." I guess we will have to retire it to steam locomotives and the like.[...]

Wait, that's not what I said! :-)

You might want to read a book called The First Three Minutes. It deals with the thermodynamics of the early universe.

 

[stevmg]

I don't follow your logic, can you please explain? Carnot's principle, which leads to the definition of entropy, does indeed apply to the entire universe and does not require equilibrium.

Edit: this thread may be more appropriate in Classical Physics. Or not, depending on the response...

Wait, that's not what I said! :-)

You might want to read a book called The First Three Minutes. It deals with the thermodynamics of the early universe.

Did I open a can of worms! I get it... Messr Carnot was "right" even in a non equilibrium universe. No more need to be explained. I shall check the First Three Minutes out of the library.

That's as far as I want to go for now. Further discussion of thermodynamics will be done in the classical physics threads.

stevmg