Exploring Atom Density of Aluminium at Different Temperatures

  • Thread starter alfredbester
  • Start date
In summary, the conversation discusses the calculation of the atom density of aluminium at 600K using the Debye model. The result obtained is 2.24x10^28 m^-3, which is significantly lower than the true density of aluminium at 2700 kg m^-3. The discrepancy is explained by the fact that the atom density only accounts for the number of atoms vibrating at a specific frequency, rather than all atoms in the material. This suggests that the Debye model may not accurately predict the density of aluminium at high temperatures.
  • #1
alfredbester
40
0
Hi, I appear to have lost some mass/density.

Q: Calculate the atom density, n, of aluminium at 600k.

Data given (some of it not relevant to this part of the ? but i'll post it all).

The debye temperature [tex]T_D = 428 K[/tex] . The velocity of sound at room temp, [tex] v = 5100m s^{-1}[/tex]. The interatomic spacing a = 405pm, and its relative atomic mass is 27.

I found the atom density n to be:

[tex] n = (KT_D / \hbar v )^3.(1 / 6\pi^2)[/tex]

I used [tex]{\omega_m}^3 = 6\pi^2 v^3 n[/tex], and the fact [tex]{\omega_m} = K T_D / \hbar[/tex] to get my equations for n.
I assumed the atom density was the same at 600k as at room temperature (the way the question was worded I couldn't see any other method). Plugging the numbers in I found [tex]n = 2.24x10^{28} m^{-3}[/tex].

Then I'm asked to compare the density found with aluminiums true density of [tex]2700 kg m^{-3}[/tex] and explain any difference.
My density is just the atom density multiplied by the atomic mass (assuming the mass is just contained within the aluminium).
Therefore
[tex]/rho = n m(amu) = n = 2.24x10^{28} * (27 / 6.022x10^{26})) = 1000 kg m^{-3}[/tex].

There in lies my problem. I'd expect my approximations to overestimate the density if anything.
 
Last edited:
Physics news on Phys.org
  • #2
Is there anyway my density could be right? Maybe some assumption of the debye model I'm not aware of. I've got the formulas straight out the textbook I don't see how it could be wrong and it's the right order of magnitude.
 
  • #3
Just had a thought is the atom density n, the number of molecules vibrating at [tex]{\omega_m}[/tex] / volume. Guess that would explain why the density is significantly lower, since many atoms won't be vibrating at [tex]{\omega_m}[/tex].
 

1. What are some common mistakes that can lead to errors in my experiments?

Some common mistakes that can lead to errors in experiments include using contaminated materials, not following proper protocols or procedures, not calibrating equipment correctly, and not properly recording data.

2. How can I troubleshoot my experiment to figure out where I went wrong?

To troubleshoot an experiment, start by reviewing your procedures and data to identify any potential sources of error. You can also try repeating the experiment with slight variations to see if you get different results. Additionally, consulting with other scientists or experts in the field can help identify any potential issues.

3. What steps can I take to ensure the accuracy and reliability of my experimental results?

To ensure the accuracy and reliability of your experimental results, it is important to carefully plan and design your experiment, use proper controls, and repeat the experiment multiple times to ensure consistency. It is also important to properly analyze and interpret your data and to conduct peer review and replication studies.

4. How can I prevent mistakes in my experiments in the future?

To prevent mistakes in your experiments, it is important to carefully plan and design your experiment, follow proper procedures and protocols, and pay attention to details. It is also helpful to regularly review and double-check your data and results, and to seek feedback and advice from other scientists.

5. What should I do if I am unable to identify where I went wrong in my experiment?

If you are unable to identify where you went wrong in your experiment, it may be helpful to seek the advice of other scientists or experts in the field. You can also try repeating the experiment with slight variations or conducting additional control experiments to help pinpoint any potential errors. It is important to also carefully review and analyze your data to see if any patterns or inconsistencies can help identify the issue.

Similar threads

  • Introductory Physics Homework Help
Replies
26
Views
779
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
946
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
5
Replies
170
Views
4K
Replies
19
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
986
  • Introductory Physics Homework Help
Replies
9
Views
1K
Back
Top