Ok , I have been studying the ideal gas law and its variants for a little while.

Now I am trying to understand how this applys to cooling systems.

For example the basic/simplified version of a refrigerator
has Compressor , Heat-exchanging pipes outside the unit, Expansion valve
Heat-exchanging pipes - inside the unit
Refrigerant ( CFC , ammonia ,...or other variants)

What I don't get fully is the process.
The compressor is changing both the pressure and volume that the ammonia has. (Since the compressor is compressing the volume that the ammonia has which in turn raises the pressure.)
From PV = nRT this implies since the number of moles n and the constant R don't change the Temperature T must go up. So this means the outside exchange pipes will dissipate the heat back down to room temperature.

But what makes the ammonia get colder again on the inner exchange pipes?

 

Expansion into a larger volume and lower pressure.

BTW, I think you are talking about Freon, or another refrigerant of this type. The ammonia cycle is quite different.

 

Expansion into a larger volume and lower pressure.

Not sure I understand this
since PV = nRT if V goes up and P goes down enough T may stay the same mathematically ?

Question 2
how do you know the Refrigerant will provide the right amount of temperature change to provide a steady 35 to 37 degrees for the refrigerator and below 32 for the freezer.

Is their some mathematically equation for the number of heat exchange coils for a given temperature based on what refrigerant you use?

 

Question 2
how do you know the Refrigerant will provide the right amount of temperature change to provide a steady 35 to 37 degrees for the refrigerator and below 32 for the freezer.

The idea is that the refrigerant can cool significantly below the desired internal temperature. The thermostat controls the compressor so the temperature stays in the desired range.

 

Not sure I understand this
since PV = nRT if V goes up and P goes down enough T may stay the same mathematically ?

You are right. If the change is adiabatic (very slow) the temperature will stay the same. However, the pressure drop in a refrigerator is precipitous. It is also never allowed to reach equilibrium as it is being compressed as quickly as it is released so the low pressure on the cold side is never allowed to rise.

 

Is their some mathematically equation for the number of heat exchange coils for a given temperature based on what refrigerant you use?

Yes, the same one. PV=nRT

Which yields (ideally) ΔT=ΔPV/(nR)

Edit: I should mention that this is a huge simplification and assumes no state change takes place, or the refrigerant does no undergo being dissolved into or absorbed by another substance. Both of these complications can and do come into play in real word refrigeration.

 

Well , my many problem is
T = P V / nR

In a compressor as the pressure goes up the volume that the refrigerant is in goes down.

Since the n and R can be taken to be constant.
This implies that the temperature could stay the same , go down , or go up.
Depending on how P , and V rate of increase/decrease goes.

How do you know that the pressure will be proportionally much greater then the volume decrease ?
For example
If they are increasing/decreasing at the same rate then the temperature will stay the same.

Question 2
Also how does one know what chemical's to use for a refrigerant?
Or in other words what would be the ideal properties for a refrigerant to have.

Question 3
You had mentioned that the pressure drop in a refrigerator is precipitous but how does the speed at which the pressure drops effect anything? Since at the same time the volume is decreasing.

 

compressing a gas heats it up.

Use a hand operated air pump and inflate a bicycle tire. Then put your hand on the bottom portion of the air pump cylinder. Be prepared, it WILL be hot. Some of the heat is from friction with the piston, but the majority of it is from the compression of the gas(air).

in refrigeration the gas is compressed into the coils on the back of the refrigerator. These coils are covered with many metal fins and serve to radiate away the heat of compression. If this heat was retained, then the gas would merely assume it previous temperature upon being released into the expansion coil. This heat is however allowed to escape, so the gas cools to a much lower temperature when expanded than it had before compression.

 

My problem is when you compress something like gas ,...etc
you are changing both the volume (decreasing) , pressure ( increasing ) at the same time.

Going by T = PV/nR would only change the temperature if the product of PV increases significantly .

But how can you be sure that it will increase and increase high enough to change the temperature high enough to effect anything.

Remember as pressure goes up volume would be going down. Even if the speed at which you do it increases both rates for pressure and volume will increase/decrease accordingly?

This is my main failure to understand why the temperature changes
And the magic behind refrigeration

So it must be the rate at which the pressure increases to volume decreases is much faster and nonlinear
But how would one know what gas would give these properties. Confused

 

You may be overthinking this. Consider that compressed gas refrigeration is quite commonplace. Removing the heat of compression is the magic that lets it work. Works for freon, H2S, and even CO2 systems.

 

Or even nitrogen. How do you think liquid nitrogen is made? You compress the gas till it is liquid and dump the heat in a multistage process.

 

ok, but I want to know why the math doesn't work out?

When you compress a gas enough it will become a liquid ( I believe this is always true )

But the formula for ideal gas (which can be a good approximation of most gases under consideration)

PV = nRT => T = PV/nR how do we know what temperature will be given off by compressing it at a certain rate? Since P goes up but V goes down at the same time. (repeating myself here)

Mathematically the temperature can only increase if the Pressure P goes up much more faster then the volume goes down.
But how do we know this will be true we would need an equation for pressure in terms of volume decrease.

Or since P = F/A => PV = (F/A)* V = F*L where L is length , A = area , F =force
So if we had a perfect volume cylinder being compressed then if we had a equation for the force interms of the length then we could take calculate the Temperature this way. Either way the key is to have some type of equation for PV rate of increase/decrease or some variation of it.

Their must be away to approximate the change in temperature mathematically by the formula above or some variation?
I know you can just measure stuff with a thermostat I would like to have a mathematical way to determine given a gas how much temperature change it will produce given the rate of compression?


Question 2
What stops the temperature from dissipating back thru the opposite side of the compressor and heating up the cooling coils at the same time as the heat going thru the hot coils. (this would defeat the purpose of cooling in a refrigerator )

One of the laws of thermodynamics state that it will try to distribute heat/cool evenly among the object under consideration until it reaches equilibrium I believe. Correct me if I am wrong.

Sorry for repeating a few things but I don't believe I have run across anybody that can answer this fully in depth.
And clear up the mathematical issues I am having.

I agree with you it works and the examples like liquid nitrogen,..etc that Bill_Marsden and others posted are good examples but their is no mathematical way I can deduce this other then using an experiment with a thermometer for every different gas I need to consider ...etc

Their should be a formula or a proof that temperature change will occur using PV = nRT or some variant

 

When you compress a gas enough it will become a liquid ( I believe this is always true )

Not quite - http://en.wikipedia.org/wiki/Critical_point_(thermodynamics)

 

Ok my mistake about that assumption but that shouldn't matter the question still stands for PV

And the second equation for refrigeration still stands

 

Mathematically the temperature can only increase if the Pressure P goes up much more faster then the volume goes down.

This is what happens. It you suddenly compress a volume of gas by one half, the pressure more than doubles, and as is obvious from PV=nRT, it gets hotter. This temperature increase is due to the work being done on the gas. However, this is not the only factor in creating the heat on the hot side of refrigeration. You do have a compressor, but the volume on both the 'hot' side and the 'cold' side are fixed. The compressor compresses refrigerant into the fixed volume of the condenser coils where the heat is released to the surrounding air.

Question 2
What stops the temperature from dissipating back thru the opposite side of the compressor and heating up the cooling coils at the same time as the heat going thru the hot coils.

Insulation. The hot side and the cool side are insulated from each other. Is this not an obvious solution?

Their should be a formula or a proof that temperature change will occur using PV = nRT or some variant

I'm not sure you are thinking correctly about the physical configuration in a refrigeration system.

Have you seen this?
http://en.wikipedia.org/wiki/Refrigeration

And this?
http://en.wikipedia.org/wiki/Vapor-compression_refrigeration

And this?
http://en.wikipedia.org/wiki/Carnot_heat_engine


This covers most of the math.
http://en.wikipedia.org/wiki/Carnot_cycle

 

You say that when you compress a gas it volume decreases.

But what if you have a fixed volume; a coil that has only X cubic centimeters of space?

In this case the volume of the gas does not change, only its pressure and temperature is changing. The volume stays the same.

So you have a cold side coil of X capacity and a warm side coil of similar capacity. These 'containers' do not change in size, so only the pressure and temperature can be changed. The 'V' variable of your equation becomes a constant number and is no longer variable.

 

You say that when you compress a gas it volume decreases.

But what if you have a fixed volume; a coil that has only X cubic centimeters of space?

In this case the volume of the gas does not change, only its pressure and temperature is changing. The volume stays the same.

So you have a cold side coil of X capacity and a warm side coil of similar capacity. These 'containers' do not change in size, so only the pressure and temperature can be changed. The 'V' variable of your equation becomes a constant number and is no longer variable.

Ok, if the volume stays constant then I guess my problem is in understanding how the compressor works. Thought it compresses the gas by decreasing the volume that the gas is in , like one of those basketball or bike pumps. If so doesn't this change the volume ?

 

It works by removing gas from one coil and pushes it into the other coil(compresses it)

The volumes are always the same in the two coils. One is always at a low pressure(and low temperature) and the other is always at a high pressure(and a high temperature)

The coil that is cold will absorb heat from its environment(the inside of the refrigerator). The coil that is hot will release heat to its environment(the outside of the refrigerator)

The heat content of the gas due to the compression or expansion is a constant(nearly so) because the volume of the container is a constant and the amount of gas is a constant. Only pressure and temperature are changing, but they change in direct ratio to each other. The total entropy of the closed system remains the same. The heat that is absorbed from the interior of the refrigerator is an ADDITION to the heat produced by compression. This heat is allowed to escape from the hot coil. This is the means of moving heat from inside the box to the outside of the box.

This is why the compressor quits running after awhile. The interior assumes the same temperature as the cold coil, therefore no addition heat is added to it. The warm side releases the same amount of heat every time(the minimum amount in this case) and the expansion side assumes the same low temperature every cycle. If the environment is ALREADY at that temperture then no additional heat is added to the cold side. Therefore the compression side always starts its compression cycle on a gas at the same temperature and ends up with a compressed gas at a specific temperature. That heat of compression is released and the cycle continues endlessly always producing the same low temperature on one side and the same high temperature on the other.

Change either side and you change the other. If you open the door of the fridge you let heat into the space. The cold coil now has a higher temperature at the start of compression and therefore the compression(hot) side will be at a higher temperature as well, since compression started from a higher temperature state on the cold side. This higher temperature on the hot side, is in relation to the outside environment(lets assume its the 78 degree room temp of your apartment). Since the difference in temperature is now GREATER between the hot coil and the air in your apartment, more heat will pass from the coil into the environment of your apartment. That heat is the heat removed by the coil INSIDE the refrigerator. The heat has gone from inside the box to the outside.

NOW your room air conditioner will have to transfer that heat from inside your apartment to outside your building.

 

The heat content of the gas due to the compression or expansion is a constant(nearly so) because the volume of the container is a constant and the amount of gas is a constant. Only pressure and temperature are changing...

Ok , I see so the volumes are fixed.
But won't the compressor keep pushing more numbers of moles of gas into the fixed volume to increase the pressure?

If that is the case then the n (number of moles is not constant)
And T = PV/nR would not just depend on P but also n???

Basically how can a compressor compress a gas (change it pressure) if it doesn't vary the volume or number of moles being put into the volume?

Basically what mechanism is the compressor using to move the gas around what force is it using/where does it get this force, and what electromechanically part is it using to do this work? I am assuming some electromechanical device in the compressor is doing something.

I get the insulation stuff
Basically the inside absorbs the heat and the outside coils disabate the heat into the room. And the insulation between the to keep it so that the rate at which the hot coils disabate heat back to other side of the compressor / the inside coils is negligible. And visa-versa. A refrigerator can be thought of in this way as a backwards heater. To the outside room it is a heater and to the inside it is a cooler.

I still am curious if their is a general formula for given a gas/liquid determine how much temperature change it will give off given the speed, rate of compression , volume sizes ,...etc.

For example if I have air as my gas , a volume that is 1cm to 1mm , and a rate of 2 gallons per second of air flow.
How much heat or temperature change can be achieved ? (note this is an example and it may be missing some variables)

Or is the only way experimentation / trial by error with different gases/liquids

 

A valve with a spring putting pressure on one side of the opening mechanism is in the line. When the compressor builds up enough pressure in the hot side coil. The valve opens slightly and small amounts of gas are let into the cold side. This is happening continually. The hot side is being compressed, by gas being added to it, and the cold side is being expanded, by gas being let into it.

The compressor is continually taking gas from one coil and pushing it into the other. The "expansion" valve is continually leaking some of that gas back into the other side.

This really is not that hard of a concept. Simply allow yourself to believe this is the truth.

The amount of gas being added into a coil is small in relation to the total volume of the coil. The gas under compression has sufficient time to release heat to the metal walls of the hot coil before it is allowed to re-enter the cold side.