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Statistical Mechanics

Posted: Fri Dec 14, 2007 5:23 pm
by bclaw2011
My project may inovlve use of statistical mechanics. I am trying to find a way to combine Charles' Law and Boyle's Law. My chemistry teacher already told me that the useo f the combined gas law was not effective enough. If anyone can be of any assistance to this problem, please respond. Please and thank you!!! :D

Posted: Sat Dec 15, 2007 11:59 am
by tdaly
I really don't understand why the combined gas law is "not enough." It is a combination, in my understanding, of Boyle's Law and Charles' Law.

Hopefully someone more well-versed in chemistry will chime in with an explanation...

Posted: Sat Dec 15, 2007 8:31 pm
by Amber_MIT
You could do an experiment with gases to see how closely the results are to the ideal gas law and Charles's and Boyle's laws. There are many statistical mechanic and thermodynamic equations/relations that were created because of the non-ideal nature of gas (deviations from the ideal gas law). Looking at gases at different temperatures would be interesting. At low temperature and high pressure (when they are close to becoming liquid) gases deviate a lot from the ideal gas law.

You could look at a few common gases and measure pressure vs. temperature and pressure vs. volume while keeping the number of moles constant. I don't know how much access you have to equipment that would allow you to measure such things. You could then see how well your results relate to the ideal gas law and see if you can account for deviations with non-ideal thermodynamic equations.

If you want to do an in-depth project, you might want to look at thermodynamic books for college undergraduates. Some of the things might be too advanced for you, but other things you could learn in short amount of time. (Fugacity has the units of pressure and is used to predict a gas's deviation from the ideal gas law, for example).

I'm not exactly sure what you are looking for, so if you can give us more information, we can try to help you more! Good luck!

Thank You Amber

Posted: Mon Dec 17, 2007 6:08 am
by bclaw2011
Thank you so much Amber for that suggestion. Unfortunately, I have no access to any gases . That was just like my initial project I thought of in October. It had to be canceled because my school and/or no one in Brunswick can afford to buy those gases. :D

Posted: Mon Dec 17, 2007 12:06 pm
by Amber_MIT
So are you going to try and do something completely different? I suppose you could do a data analysis project, looking at data people have already gathered about gases and see how and why they deviate from the ideal gas law, though it would probably be easier just to do something else.

If you have no idea where to start looking for another project, visit the science buddies topic selection wizard to help get you started. http://sciencebuddies.org/mentoring/register_guest.php

You could do a variation of some of the sample projects to make them at a high school level. If you don't want to do the topic selection wizard, you can just browse the projects here: http://sciencebuddies.org/mentoring/project_ideas.shtml

Good luck and if you have any more questions on the project you do end up choosing, post questions back on here if you need help!

Possibilties

Posted: Wed Dec 19, 2007 1:06 pm
by bclaw2011
But is it possible to convert the results I receive from the Boyle's Law and Charles's Law and apply it to the atmosphere :?:

These two projects at these sites were combined:

http://www.sciencebuddies.org/mentoring ... ?from=Home
http://www.sciencebuddies.org/mentoring ... p011.shtml
Please view these before resopnding. :D

Conclusion Structure

Posted: Wed Dec 19, 2007 1:09 pm
by bclaw2011
If not, can anyone help me come up with how the use of Boyle's Law and Charles's Law effects the world besides the atmosphere :?:

Posted: Wed Dec 19, 2007 4:48 pm
by bclaw2011
The two messages above were meant for my other message. Sorry if I confused anyone. :lol:

Posted: Wed Dec 19, 2007 4:57 pm
by Amber_MIT
FYI,

I have a final exam tomorrow so I need to study for that but I will get back to you as soon as I can after I'm done.

Posted: Wed Dec 19, 2007 5:41 pm
by bclaw2011
Good luck on your finals, Amber :!: :D

Desperation

Posted: Wed Dec 19, 2007 6:29 pm
by bclaw2011
I really badly want to go all the way to internationals in Atlanta this year. I think I have a really good project, it's just missing something. I have combined two projects that are available links:
http://www.sciencebuddies.org/mentoring ... ?from=Home
http://www.sciencebuddies.org/mentoring ... p011.shtml
I have decided to perform the variation which is why this post is called Statistical Mechanics.
I am however very interested in the data analysis experiment suggestion you posted about looking at data people have already gathered about gases and see how and why they deviate from the ideal gas law.
If I could do this project, do you think it could be a good one :?:
And if I do it, where do you think would be the best place to retreive this information :?:
Can you kinda get me started :?:

Posted: Fri Dec 21, 2007 2:28 pm
by bclaw2011
I have just discovered some more research and I know which statistical mechanic ensemble to use- the isobaric-isothermal ensemble or it might be the canonical ensemble. I just need to find out how to use it. Can anybody help me, please :?:
http://en.wikipedia.org/wiki/Isothermal ... c_ensemble
http://en.wikipedia.org/wiki/Ideal_gas_ ... _mechanics

Re: Statistical Mechanics

Posted: Mon Dec 31, 2007 4:21 pm
by Amber_MIT
I hope you had a good holiday!

To answer your questions:

I think you would learn a lot from doing a project like this. I must warn you, however, that competing at a high school level, many students do more original research. I don't know how competitive it is to reach "internationals" in your area , so it is difficult to say whether this will be a good project for you or not. You seem to be very interested in it, which is a huge advantage. If you don't like the subject matter then you won't enjoy doing the project. There are always possibilities for making your project more original and adding some creative things to it, these types of things normally happen while working on the project and are difficult to just magically think up. I have looked at the science buddies project ideas you gave me, and I have a general idea of what you want to do, but if you want to give me more specifics I could help you further.

Wikipedia is a great source to start looking for information, but the science and math sections are difficult to understand if you've never studied the material before. I would go to a library and get a thermodynamics/kinetics textbook that chemical engineers would use. We used "Thermodynamics, Statistical Thermodynamics, and Kinetics" by Thomas Engel and Philip Reid but it is NOT a good book and I would not recommend it (so stay away from it!!! :-). A book I would recommend is: Introduction to Chemical Engineering Thermodynamics by J. M. Smith, Hendrick C Van Ness, and Michael Abbott. It is relatively dense but it has many things that would be useful to you. Research FUGACITY, which will help you tons. If you ask most people what "fugacity" is they will probably say "it has the units of pressure." Unfortunately not many classes really go into what it actually is ("Oh, there isn't a physical example for it" they'll tell you). After learning about it I can tell you that it is a mathematical term used to explain deviations from ideality. So, people essentially made it up to explain these deviations. It's a a term people use to help model a gas's behavior. Once you do some more research and understand the background information a bit better, you will better know how to model gas behavior. I'm not a huge expert in this area, I've only taken one class in it, but I can at least guide you in the general direction that would make sense to research.

As for a good place to get some data, go to NIST: http://webbook.nist.gov/chemistry/fluid/

At the above website you can look at graphs for certain temperature and pressure ranges. Play around with it a bit and see what happens when you change things.

For general properties about certain compounds, go here: http://webbook.nist.gov/chemistry/form-ser.html

For the main page go here: http://webbook.nist.gov/chemistry/
The two websites above were from the "Thermophysical Properties of Fluid Systems" and "Formula" (under the "Search Options") links.

I hope that helps!

Re: Statistical Mechanics

Posted: Wed Jan 02, 2008 7:40 am
by bclaw2011
Thank you Amber for the sites, but I have decided to stick with my project. Thank you for being a great help. But I want to ask you if you wouldn't mind if I quote your science experiment ideas for my conclusions.

Re: Statistical Mechanics

Posted: Wed Jan 02, 2008 8:17 pm
by Amber_MIT
bclaw2011 wrote:Thank you Amber for the sites, but I have decided to stick with my project. Thank you for being a great help. But I want to ask you if you wouldn't mind if I quote your science experiment ideas for my conclusions.



I don't mind at all. Good luck with your project!