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ibysaiyan
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Homework Statement
Hi all, I have been trying to go over this problem for sometime now.. yes I have easily browsed over +200 articles, lectures , etc on google.
The question is related to delong petit law and wants me to find out the temperature at which it fails i.e when quantum effects prevail ( In this it's aluminium).
Homework Equations
Aluminum = 27g/mol
The Attempt at a Solution
At higher temperature specific heat of solids is roughly ~3R but all this changes of course with drop in temperature , Cv tends to -> 0.
Now I have made few assumptions and have ended up with two values of temperature one is 161kelvin and other being about 50k which I are probably too high. Anyways...
From what I know is that as temperature drops so does the no. of degrees of freedom.
According to equipartition at room temperature we get 3RT but it's my intuitive feeling that at lower temperatures D of freedom is 2 ( due to vibration ? )
So over all energy is = KbT , another variation of it can be :
Δ E = hω.
Now here is one of my attempt.
Δ E = hω
KbT = hω
T = hω / kb (i)
w = 1/2pi * {square root of k/m}
w = 3.36*10^12 Hz plug this int eq. (i)
T = hw/kb
T = ~161kelvin...
On the previous part spring constant 'k' was given as 20 N/m however I am not sure if I am meant to use it for this question since in the previous bit temperature was '300k'.My other approach was to use: 24.9 > dE/dt
24.9 > KbT/ (t-300)
P.S: I have not slept through the night it's 9 am now, feedback of any kind will be appreciated. Thanks
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