Algebra and Absolute Zero

[Atomic_Sheep]

If we take a gas thermometer and cool it to absolute zero, the pressure vanishes. What happens to volume? The way I see it, it can't be zero, however on a PV vs T graph, 0 x V = 0 so volume can be anything but at the end of the day the 0 pressure multiplies by volume and yields 0.

 

So, here's where the algebra comes in that I'm getting confused over...

 

Comparing two gas thermometers (one much larger than another) both initially at room temp... the first one is of a volume of 1m^3 and is argon and another one we have equaling to 5cm^3 and is helium. Then they are both cooled. At some point your pressure goes to zero, whatever that means because how do you even measure the pressure of these gasses at such low temps (in fact this is the third question), then we get PV = 0 for both thermometers but how are you sure that both are at the same temperature if we're looking at two very differently sized cubes?

 

So the first question is 0 x X = 0 and 0 x Y = 0 the volumes are non zero for both yet the formula suggests they are zero???

 

The second question is... how do you know temperature stops going any lower just because the volume seemingly stops to decrease?

 

Third question is, how do you measure such pressures?

Edited March 24, 2015 by Atomic_Sheep

[swansont]

Typically in these problems you hold one value of P, V and T fixed, and let the other two vary. One might physically maintain e.g. constant volume by having the gas in an appropriate container, e.g. glass or metal. (rather than a balloon). One thing to look at is what is happening as you lower the temperature, when its value is nonzero — if P is going down proportionally, then V has to be constant for PV vs T to be a straight line. It's been constant the whole way, so it isn't going to change for that last data point — if it were meaningful. You should be aware that this situation is not physically realizable; you can't actually get to absolute zero.

 

Temperature is independent of the sample size, as it's a measure of the average kinetic energy of the atoms or molecules.

 

One way of measuring temperatures of a cloud of atoms is to contain the atoms (you can do this magnetically) and then release them, and imaging the cloud to measure its expansion. That tells you the average speed of the atoms, which is related to the temperature. This is a method used with Bose-Einstein gas condensates, which can get down into the nanoKelvin temperature range.

[ajb]

There is nothing wrong with your algebra here. But two points need to be made.

 

i) absolute zero cannot be reached using only thermodynamic means. The system will tend to absolute zero.

ii) absolute zero is taken as an extrapolation of the idea gas law. Gases will show deviation from this law as they are cooled.

[mathematic]

There are no substances which are gasses near absolute 0. The closest is He which is liquid. Everything else is solid.

Edited March 25, 2015 by mathematic

[swansont]

There are no substances which are gasses near absolute 0. The closest is He which is liquid. Everything else is solid.

 

You should check out Bose-Einstein condensates. They are gases, near absolute zero.

http://en.wikipedia.org/wiki/Bose–Einstein_condensate

[imatfaal]

 

You should check out Bose-Einstein condensates. They are gases, near absolute zero.

http://en.wikipedia.org/wiki/Bose–Einstein_condensate

 

How cold is the caesium (ruibidium?) in the fountains of your clocks

[swansont]

 

How cold is the caesium (ruibidium?) in the fountains of your clocks

 

Our rubidium "only" gets down to a couple of microkelvin. The cloud expands with the atoms moving at an average speed of a few cm/sec

 

Funny thing is, that didn't immediately pop into my head because I'm aware of the atomic physics efforts in these areas, I no longer think of microkelvin as being particularly cold, because we tend to look at this logarithmically, i.e. once you get down to low temperatures, knowing that zero is the asymptote, you think in factors of ten reduction rather than differences. So there's a mindset that a nanokelvin is a lot colder than a microkelvin when it really isn't, in absolute terms. But because of the hard limit, the effort required to get that much colder is quite large.