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- 1.
- For some system the dependence of the probability of micro-state
on energy was obtained for different temperatures:

Check all statements that apply:- (a)
*T*>_{1}*T*>_{2}*T*_{3}- (b)
*T*>_{3}*T*>_{2}*T*_{1}- (c)
*T*>_{2}*T*_{1}- (d)
*T*>0_{3}- (e)
*T*<0_{3}

**Solution:**- Since , the log of
probability depends on
*E**linearly:*- If
*T*>0 this is a decreasing function, so*T*>0,_{1}*T*>0,_{2}*T*<0_{3} - The greater is
*T*, the less steep is the line (what happens if ?), so*T*>_{1}*T*>_{2}*T*_{3}

- If

- 2.
- Prove that . What happens with fluctuations in the thermodynamic
limit?
**Solution:***A*is an*extensive value*,*X*is an intensive value. Therefore at the scaling is , , ,...We obtain:

and

© 1997

Tue Sep 9 22:39:08 EDT 1997