Physics thermodynamics question on thought experiment.

[studiot]

A 1k body is totally isolated in its own universe.

 

What is its temperature, consistent with the laws of Physics?

[swansont]

1k?

 

[studiot]

Sorry a body of one kilogramme mass.

[swansont]

OK. Still not enough information.

Spoiler

A body will radiate energy according to its temperature (T^4), so the temperature of the object will decrease with time, approaching zero (since an empty universe is effectively at 0 K; there are no photons to be absorbed). No conduction or convection to worry about.

 

[Sensei]

I think so there is still not enough information.

Objects with different shapes will radiate photons differently.

See difference between Aluminium heat sink with large area, and f.e. Aluminium sphere with [math]4 \pi r^2[/math] area.

 

[Carrock]

0K and in a low(est) energy configuration.

Otherwise it would have radiated photons and wouldn't be isolated.

[Sensei]

43 minutes ago, swansont said:

there are no photons to be absorbed).

It depends on shape of object. If photons will be radiated by heat sink internal piece they can be reflected or absorbed by another piece.. Spherical object won't have this "problem".

 

47 minutes ago, swansont said:

No conduction or convection to worry about.

Conduction and convection will happen inside of our object. Before being radiated as photons to environment around it.

Imagine heat sink connected with sphere together. Heat sink part will be emitting photons at different rate than the rest of sphere.

 

Also we should ask question whether object is made of uniform material, metal, or couple different materials,

or it's radioactive material, decaying (and heating it inside, like it's happening with Earth's core).

[J.C.MacSwell]

It would depend on the size and metric of this universe would it not?

I guess if it is a 1 kg "mass" that might put limits on what is possible...

It could reach equilibrium, or not, at or from almost any temperature where the matter itself is stable

If, say, it was isolated (read remote) in this Universe it would be at or heading toward 2.7 K

Edited October 5, 2017 by J.C.MacSwell

[studiot]

I am not trying to hide trick information here.

Sensei, So let us assume there is no radioactivity in play - say the mass is iron.

Carrock, there is nothing to prevent thermal radiation is there. I did say that test universe was isolated, not the mass. 

MacSwell, I am not looking for accurate numbers just ballpark.

 

Thank  everyone for answering and hope you will continue to discuss,

I hope the question is stimulating - it has relevance in cosmology - I am interested in the physical arguments you would employ to arrive at a conclusion.

 

 

 

 

[Mordred]

You still need something to correlate a density to equate the temperature even if you are using specific volume. Are we assuming pressureless dust?

Ok iron is 7874 kg per m^3 @ 20 degrees. One can simply apply the ideal gas laws from here.

Edited October 5, 2017 by Mordred

[Carrock]

3 hours ago, studiot said:

A 1k body is totally isolated in its own universe.

 

What is its temperature, consistent with the laws of Physics?

 

41 minutes ago, studiot said:

Carrock, there is nothing to prevent thermal radiation is there. I did say that test universe was isolated, not the mass.

If the mass is not isolated from its test universe, then its temperature depends on that universe's state. I don't think e.g. a static universe is consistent with current physics.

I'll assume the universe is much like ours, and that it will continue to expand for unlimited time.

Choosing a random time, I'd expect the temperature of the mass to be very close to 0K as our cosy universe with stars and people exists for a negligible fraction of unlimited time.

 

Quote

I am not trying to hide trick information here.

I don't believe anyone thinks that, but any reply requires a lot of assumptions; a question where all the assumptions are explicit wouldn't be any fun to respond to!

[Mordred]

I'm assuming the specific volume is the total volume of the toy universe. Hence needing details to correlate a density to the mass term. Though Studiot stated assume iron.

under assumption of specific heat 460.5 joules/kg-k

However this is under assumption of specific volume/heat relations. Heat is not temperature 

(the above is not temperature it is the amount of energy required to raise iron 1 degree)

However I am waiting to see if I'm on the methodology Studiot is describing.

If I'm right he is indicating that there is a difference between heat and temperature.

At least I hope so as it is an incredibly important lesson in physics.

Edited October 5, 2017 by Mordred

[studiot]

T

1 hour ago, Mordred said:

However I am waiting to see if I'm on the methodology Studiot is describing.

There's no right answer here or else everyone is right.

swansont was (as usual) really quick off the mark and happened to put what I was thinking about in his spoiler.

I was thinking that the body would start to radiatiate as a black body within its universe. The radiation couldn't leave the universe because of the isolation.

My first thought was that it would cool to absolute zero if one could wait long enough but on second thoughts life is more complicated.

But where will the radiation go?

Into the empty surroundings I suppose.

This will raise the background temperature of the otherwise empty surroundings a fraction, rather like the background in our own universe.

The loss of energy from the body will also cool the body somewhat.

So there will be an ever diminishing temperature differential between the body and its surroundings, so it will cool at an ever decreasing rate and never actually reach absoulte zero.

The cooling will be asymptotic to some low temperature above zero, where a balance exists between the cooling radiation and warming radiation from the background.

This is rather like the discharge of a capacitor over time.

 

My comment about the link to cosmology is "doesn't this look rather like the big bang in many ways?'

 

Others may have equally valid (or even better)  ideas.

Edited October 5, 2017 by studiot

[Mordred]

gotcha, I noted Swansonts spoiler, but thought of a different scenario where the body itself was the universe. So no potential for loss.

Glad I waited

[MigL]

From QM considerations, it could never get to 0 deg anyway.

[J.C.MacSwell]

4 hours ago, studiot said:

.

But where will the radiation go?

Into the empty surroundings I suppose.

This will raise the background temperature of the otherwise empty surroundings a fraction, rather like the background in our own universe.

 

This was my thought  as well wrt the size and metric of this universe, and whether equilibrium could be reached (expanding, contracting, static somehow etc). No other matter to radiate back (initially at least), but maybe it all comes back, reradiates etc etc. If the universe is small enough our kg might stay nice and toasty.

[studiot]

10 hours ago, MigL said:

From QM considerations, it could never get to 0 deg anyway.

I don't see this as a quantum issue. That was also why I chose a mass of 1kg (got it right this time   ) - to avoid the issue of the body being a single sub atomic particle.

In any event temperature does not play well as a quantum variable.

 

I asked the question "Where does the radiation energy go?" and now I am asking where does it come from?

It comes by reducing the vibrations of the particles that comprise the body.
These are held by bonding forces that are electrostatic in nature.
And we know that electrostatic forces are many times stronger than gravitational ones.

So I suggest there will not be a relativistic gravitational effect in this universe, leading to an expansion, although there will be a near negligible gravitation effect on the radiation leaving the body.

Can anyone else see anything further that can be extracted from this scenario?

[swansont]

11 hours ago, studiot said:

 

My first thought was that it would cool to absolute zero if one could wait long enough but on second thoughts life is more complicated.

But where will the radiation go?

Into the empty surroundings I suppose.

This will raise the background temperature of the otherwise empty surroundings a fraction, rather like the background in our own universe.

Will it, though? The BB radiation is isotropic. The radiation from the test mass is not. The reason you use the background temperature in calculations is that an object will be absorbing radiation and you are doing a power balance. But there would be no absorption from the background in an otherwise empty universe.

11 hours ago, studiot said:

 My comment about the link to cosmology is "doesn't this look rather like the big bang in many ways?'

The big difference is noted above. Even if the temperature was high enough that you could get pair production, that requires something to conserve momentum. That can happen if you have a strong enough electric field, but probably not with a 1 kg object.

For whatever reason we had a net amount of matter in the early universe which could scatter and rescatter photons, and gave us our isotropic background. (I think you also need inflation happening at the right time.)

[studiot]

swansont, thank you for your thoughts.

5 minutes ago, swansont said:

Will it, though?

The best 'black body' we have is an empty space at the entrance to an absorbing cavity.

Would not a perfect black body be an empty space at the entrance to a perfecly absorbing cavity?

Also would not the background radiation impinge on the surfaces of the 1kg body as it floods around the universe?

[swansont]

31 minutes ago, studiot said:

swansont, thank you for your thoughts.

The best 'black body' we have is an empty space at the entrance to an absorbing cavity.

Would not a perfect black body be an empty space at the entrance to a perfecly absorbing cavity?

Also would not the background radiation impinge on the surfaces of the 1kg body as it floods around the universe?

Why would photons that escape the object return to it?

[J.C.MacSwell]

1 hour ago, swansont said:

Why would photons that escape the object return to it?

They would presumably follow a geodesic until it showed up in front of them...or not...but that would depend on the metric.

[swansont]

47 minutes ago, J.C.MacSwell said:

They would presumably follow a geodesic until it showed up in front of them...or not...but that would depend on the metric.

But I'm thinking an empty universe with a 1 kg object in it would be basically flat

[geordief]

Would the body  have a rotational momentum? Could it not have one?

 

Where would any measurements be taken? From the original centre of the body?

 

The scenario seems to ressemble a Big Bang but must surely be lacking/different  in  many ways.

 

As soon as the body starts to radiate  would it also start to re radiate back  inwardly  ?

[Sensei]

3 hours ago, studiot said:

[radiation energy]  and now I am asking where does it come from?

Hotter body has slightly higher mass than colder body. After emission of photons, mass of body is decreasing.

 

Edited October 6, 2017 by Sensei

[J.C.MacSwell]

2 minutes ago, swansont said:

But I'm thinking an empty universe with a 1 kg object in it would be basically flat

That's a reasonable assumption. Possibly the most reasonable? (I don't know)