[Murka]

Hey guys, I'm doing a lab report about the thermal conductivity of Nitrogen, Argon and Carbon Dioxide.
One of the report requirements was to plot a graph of the three on the same graph with the current squared being normalized to between 0 and 1.
The question asked is "What can we learn from this graph"?

The obvious answer would be that those gases (and maybe all gases?) behave very similarly in respect to thermal conductivity, but what else can I say about this? Can anyone elaborate?

(The graph is (Normalized I^2 in respect to Pressure) btw)

[Corribus]

Nitrogen, argon and carbon dioxide are very different.  What kinds of relationships does this experiment test?  (I.e., what are the differences between the gasses.)  I would suggest also thinking about what relationships the experiment does NOT test.  I.e., can you think of another gas that would be good to test, and what relationship you would be probing?  Perhaps hypothesize about the result based on what you know about heat conduction.

Also, units on the plot would be helpful.

[Murka]

The tests themselves are unrelated, it's a system in which I inject a gas, and then gradually pump the gas out using a rotary pump and measure the current in the reference cell (Acting as a resistor) using a wheatstone bridge. So I get different readings as the pressure goes down.

Pressure units are mmHg, current units are mA but the Y axis represents current squared so it's (mA)^2.
Obviously when not normalized, the graphs look different, but when normalized they kinda all merge into the same thing, suggesting the same behaviour.

Here is the original graph attached...top to bottom Nitrogen, CO2, Argon.

Also sorry for not including the axis titles units etc' on the graph, it's not in english so it would just confuse...

[Corribus]

What are you normalizing them for, and why are you doing it?

[Murka]

What are you normalizing them for, and why are you doing it?

Just normalizing the I^2 values for 0-1 with the (value-Minimuml)/(Maximum-Minimum) method.
The lab instructor asked for a normalized graph in addition to the regular one, and to explain what I can deduce from it.
I just doubt the only stuff I can write about this is "From the normalized graph we deduce that although the innate heat conductivity of the gases is different, the general behaviour is the same"...

[Corribus]

Well, I'd start by asking what factors influence thermal conductivity.  Both of your plots convey useful information.  It shouldn't be unexpected that if you divide each data set by the maximum value, they all approach 1.  The raw datasets are all quite different.  What do you learn from that?  And what do you learn from normalizing the data sets?   If you're struggling with that second question, ask yourself this: supposing they were different when you normalized them, what would they be likely to look like, and what would that tell you?

[Murka]

I do realize you're trying to lead me to the answer...but sadly I'm not really getting it...
If we categorize by mass then CO2>Ar>N2, by avg. free path it's the other way N2>Ar>CO2 but if we categorize by...umm...bulkiness? Atomic radii, volume? Then it's CO2>N2>Ar...

The answers are neither of those, why N2>CO2>Ar?
I know that overall the dipole moment of CO2 is 0, but still momentary dipoles still occur, could this affect the measurement?

I really need to have a plausible answer for this until saturday, and deduce what the normalization teaches us about this all.

[Corribus]

I'm not necessarily trying to lead you to an answer, because I don't really know the answer.  I could probably hand-wave one if pressed, I suppose, but that's not the point.  What I'm trying to do is help you think about the problem by explaining how I would think about the problem if I had to write a report on that data.

Thermal conductivity is not a simple thing.  For gasses (gases?) the only way to conduct heat is through collisions, so as you can imagine the conductivity is going to be dependent on the frequency of collision and how much heat a typical molecule/atom can carry.  The latter is essentially the heat capacity and the former is dependent on the average speed of gas molecules (how far they can go on average before they hit each other) and the average size (bigger molecules have a higher probability of colliding) and the concentration.  And if the gas molecules behave non-ideally, pressure is also going to affect things through the additional mechanism of molecules "sticking together" through intermolecular forces (think of water here).

Atomic gases (gasses) tend to have high heat capacities, despite their small size, because they move quickly and have a high probability of colliding.  But they can't carry much energy (low heat capacity).  Bigger molecules move more slowly but are large; in addition they have vibrations and rotations that can store energy, which means that when they do collide, the amount of heat energy they can pass along is large.  And intermediate molecules are intermediate.  What does this mean?  It means that thermal conductivity isn't necessarily something that's going to have a neat and simple relationship to one parameter like molecular weight.  Maybe you can also see why, now, your pressure dependence is pretty low, except at very low pressures (why does heat capacity tend toward zero at zero pressure?).  But the pressure dependence isn't exactly zero (why?).  What does the relative pressure-independence (especially evident in your normalized plot) tell you about the ideal or non-ideal behavior of argon, nitrogen and carbon dioxide?

Just some things to think about.  Maybe you find this useful:

http://www.cambridge.org/us/engineering/author/nellisandklein/downloads/extended/Section%201.1.2%20Thermal%20Conductivity%20of%20a%20Gas.pdf

[Murka]

So, from what I understand from your explanation is that thermal conductivity isn't simple and is affected by many many factors...

The instructor's question now makes more sense, as it IS an interesting question as why despite all those factors, normalizing the three gases' values still gives a uniform graph, how does normalizing "reduce" (as in math), all those factors into the same thing?

Still have no answer for that...

[Corribus]

Normalizing a plot of x vs y for several datasets erases information about how the absolute magnitude of the dependent variable (y) at any given value of the independent variable (x) varies for each dataset.  However it makes it much easier to compare how the magnitude of the dependent variable changes as a function of the independent variable (or for some other important variable) for two (or more) data sets.  The two types of plots give different information.

In this specific case, normalizing the plots erases information about which gasses have higher or lower thermal conductivity.  However, it makes it much easier to see whether there are differences in how the conductivity varies - relatively speaking - as a function of pressure for the different gasses you are looking at.  The data shows that even though the three gasses you looked at have different absolute thermal conductivities, the relative pressure dependence of their thermal conducitivities is similar (that is, there is very little pressure dependence).

The question is: what does this tell you?  The answer is pretty much directly stated in the link I gave you earlier. 

[Murka]

Umm...
As I see from the article, K(ideal) is proportional to (Cv/(σ^2))((T/mW)^(0.5)), normalization obviously "smoothes" out those differences, but what about the pressure dependence? Does this mean that pressure dependence doesn't get normalized with the rest (Due to the equation not taking this into account), and then I deduce that since we get a similar behaviour *anyway*, the pressure dependance difference is negligible even in a non-ideal system?

[Corribus]

Nevertheless, Eq. (1-18) is useful in that it correctly predicts that the thermal conductivity of an
ideal gas is independent of pressure, but increases approximately according to the square root of
temperature. There is no pressure dependence because increasing the pressure both increases the
number density of the gas and decreases the mean free path; these changes exactly cancel for an
ideal gas. The thermal conductivity of a 'real gas' (i.e., a gas at conditions where it does not obey
the ideal gas law) will exhibit a dependence on pressure that increases with increased deviation
from ideal gas behavior.

To a first approximation, none of your gasses have a pressure dependence, so....  ?

Although, you will notice that there is SOME pressure dependence, particularly at higher pressures.  This is more pronounced in one of your gasses (to my eye) than the other two.  What might we conclude about that?  Also, I would do your normalization around a more moderate pressure (~ 100 or 150).  This will allow you to see what I'm referring to a little better.

[Murka]

What do you mean by doing the normalization around a different pressure?

[Corribus]

How did you normalize your plots?

[Murka]

Using the Y-axis I^2 values

(Value-minimum)/(maximum-minimum)