Why will this not work?

[Kayra]

If I had a 1,000 meter tall tube that was perfectly isolated thermally, and I proceeded to fill that tube with gaseous ammonia at -28 degrees C.

 

Given a dry adiabatic lapse rate of 10 degrees C per 1000 meters and boiling point of Ammonia at -33 degrees C.

 

Would the Ammonia condense on the tube surface on its journey up the tube?

 

If it did, I could collect a constant stream of condensed ammonia from a thermally isolated process, correct?

 

This seems wrong on so many levels :D , so I would like to know what I am missing. (I suspect something to do with the vapor pressure)

[Qfwfq]

Condensation will surrender latent heat. Where does it end up?

[Kayra]

Condensation surrenders latent heat, with affects the adiabatic lapse rate (rate at which the gas cools as it rises with no energy in our out.)

 

The adiabatic lapse rate past the "Dew point"? should be approximately half of the dry adiabatic rate. At least this is how it works for water vapor in air. I am not certain if the effect is the same for a pure gas.

[Qfwfq]

Thermodynamics was never my best topic but as far as I can see, the condensation influences the drop in temperature for a given drop in pressure but it can occur adiabatically. It's the reason why water vapour becomes white steam very shortly out of the kettle spout or pressure cooker valve. I don't see what's wrong with it, seems to me it's all a matter of whether the height of the tube and consequent pressure drop is sufficient.

[Kayra]

I guess my concern is a never-ending way of turning a gas into a liquid without inputting energy would violate a few laws of physics :hihi:

 

The liquid that returns down the tube (or a separate tube) is not compressible and so would not heat up as it came back down (as a gas would). It would remain at the cooler temperature.

 

This system would present an opportunity to refrigerate something by evaporating the ammonia, without using any energy. Forever.

 

Clearly this can not be correct but I can not figure out why.

 

Could it have something to do with the fact that the gas will be less dense at altitude and for that reason have a lower "Dew Point" that it would forever chase and never catch? (No condensation)

Or will the latent energy released accumulate at the top, eventually heating the gas beyond its dew point?

Is the heat being turned into potential energy because the liquid has been raised up, and then being discarded on the way down?

 

Is there some other process involved that I can not see?

 

How would you model this?

[Pyrotex]

I would like to weigh in, but I need to know:

Is the tube arranged vertically in Earth's gravitational field?

Is the interior of the tube open to the exterior environment at the top?

Is the ammonia introduced at the bottom of the tube? And pumped in?

What is lapse rate again? :)

[Kayra]

I would like to weigh in, but I need to know:

Is the tube arranged vertically in Earth's gravitational field?

Is the interior of the tube open to the exterior environment at the top?

Is the ammonia introduced at the bottom of the tube? And pumped in?

What is lapse rate again? :)

 

Yes the tube is arranged vertically.

The top is closed and the bottom is where the gas is fed in (black box) at -28 C. You can consider it pumped in, but the pressure will be 1 atmosphere.

 

Their are 2 lapse rates, the Dry one (approx 10 C/1000 M) and the Wet one (Approx 5.5 C/1000 M)

 

The gas temperature should fall as the gas rises at the dry rate until it reaches its dew point or saturation point. From that stage on the wet lapse rate would apply due to the condensation releasing latent heat.

 

 

As the gas condenses, more gas is fed in at the bottom at -28 C

[Kayra]

Hmm, those are the lapse rates for the atmoshphere.

Does anyone know how to calculate the lapse rates for ammonia?

 

These might help, but my math skills are horrible.

Lapse rate - Wikipedia, the free encyclopedia

Ammonia (NH3) Properties

[Pyrotex]

So, the tube is closed, and the ammonia is being pumped in under increasing pressure?

[Kayra]

Yes, the tube is closed.

 

But think of the tube as being made of a flexible impermeable material.

It starts completely flat and expands as it is "inflated"

Ammonia gas is allowed to enter at 1 atmosphere pressure.

 

I would have to say that the pressure is not increasing.

 

.

[Qfwfq]

I guess my concern is a never-ending way of turning a gas into a liquid without inputting energy would violate a few laws of physics :)

 

The liquid that returns down the tube (or a separate tube) is not compressible and so would not heat up as it came back down (as a gas would). It would remain at the cooler temperature.

 

This system would present an opportunity to refrigerate something by evaporating the ammonia, without using any energy. Forever.

 

Clearly this can not be correct but I can not figure out why.

I was reasoning in the short term and not on a cycle but, if you are talking about a long-term cycle it's a wholly different matter! :(

 

You need to work out the equilibrium and you are quite right in not expecting to find the principles of thermodynamics being violated. There are things you still don't specify, leaving some variety of possibilities, with details differing, and as I said I'm not so fresh on the topic. Clapeyron's equation is probably useful to your musings. The first question is, how long can you continue putting gas in without work if only liquid and no gas is coming back down? Is the liquid coming back down in thermal contact with the stuff going up?

[Kayra]

This is a component in a larger system I am working on. The gas is continiously supplied by other processes.

 

The Tube is not a closed proccess in this regard, but I still do not understand the apparent change in energy within it.

 

The liquid is isolated physically and thermally from the gas once it condenses.

 

Qfwfq, you are a lot fresher on the subject then I if you know of this Clapeyron fellow and understand his equations

 

Sadly, my abilities in this area are limited, but I will try to struggle through the references to it.

 

It would help me tremendously if someone could post an example of that formula using this gas at -28 C and 101 KPascals

[freeztar]

This is a component in a larger system I am working on. The gas is continiously supplied by other processes.

 

The Tube is not a closed proccess in this regard, but I still do not understand the apparent change in energy within it.

 

The liquid is isolated physically and thermally from the gas once it condenses.

 

Qfwfq, you are a lot fresher on the subject then I if you know of this Clapeyron fellow and understand his equations :)

 

Sadly, my abilities in this area are limited, but I will try to struggle through the references to it.

 

It would help me tremendously if someone could post an example of that formula using this gas at -28 C and 101 KPascals

 

Interesting ideas Kayra. :)

 

To use the Clapeyron equation, you'll need values for many more variables including volume, entropy, etc.

Clapeyron's Equation -- from Eric Weisstein's World of Physics

(I think this is what Q was referring to?)

 

Unfortunately, even with all the variables, I'm useless as my calculus skills are virtually non-existant.

[Kayra]

Let’s see.

Can I assume that a calculation done every meter is reasonably accurate? If so, then for the purposes of this thread we can assume the volume to be a cylinder 1 meter in diameter and 1 meter high. That makes the volume 0.785398163 cubic meters.

 

How does one calculate entropy? I can not make heads or tails out of that :)

My attempts to do these calculations always end up seriously wonky, and I suspect that not using standard units of measure is likely the culprit.

[Kayra]

OK, as a logic exercise, let’s assume that this system has a heat source at the base that will vaporize the returning ammonia liquid into a gas at precisely -28 C and that gas is released back into the base of the gas column. This would make the system cyclic.

 

Would this system require a constant input of heat, and yet remain at the same temperature. That would suggest that work was accomplished. Conceptually then, the heat energy is what is driving the flow of gas up 1000 M.

 

If this is the case, then is this a means of essentially free and continuous refrigeration?

 

As this can not be, I wonder if condensation will even occur (it certainly appears that it should), or if I am just losing track of where the energy is going.

[Qfwfq]

Qfwfq, you are a lot fresher on the subject then I if you know of this Clapeyron fellow and understand his equations :cheer:

Tee hee, I couldn't write it myself without looking it up! It's basically how the boiling point depends on pressure.

 

Now, something you don't detail is bringing gas back down as well as fluid. Unless you manage to fully condense the gas some of it will be left over, but you couldn't really do that with a pure gas. If you bring it down, in what state will it get back to the bottom? If you don't let the liquid evaporate again it can't be the same state that started the way up, in order to have a cyclic transformation the gap has to be bridged.

[Kayra]

The cyclic part was just to drive home that fact that some energy was going somewhere :confused:

 

If the gas were brought down through say a second tube, I would expect it to heat up at the dry adiabatic rate of 10 C/1000 M but the only thing brought down is the liquid. The gas is left at the top and new gas is drawn up to replace the amount lost due to condensation.