Please read my homework policy details (including lateness policy) VERY carefully.
(a) Consider a molecule which has energy levels
En=c|n| , where n is a vector with integer
components. Compute the partition function for a one-dimensional
ideal gas of such molecules. Show that the average energy (assuming
large temperature compared to the difference between adjacent energy
levels) gives U=kBT . This is twice what
was obtained for the non-relativistic molecules we studied in
class.
(b) Take c=0.5eV. For a lab-sized box of gas of our
molecules, estimate the temperature (in Kelvins) at which the
assumption of part (a) breaks down.
(c) Find the entropy. Figure
out if this expression breaks down at low temperature. Are the two
breakdown temperatures of (b) and (c) similar? Why or why not?
Even though distribution functions are very peaky about the thermal
average, fluctuations do occur at finite N. In this problem
we'll work out some properties of fluctuations.
(a) Do KK 3.4: Energy Fluctuations. (Be very explicit about explaining
each step you make in writing your solution, conceptual or
mathematical.)
(b) Then, [after we've covered phonons on wed-09-feb!] do KK4.13,
Energy Fluctuations in a Solid at Low Temperature.
Do KK4.8. [You'll need info from the lecture of mon-07-feb.] Also, try to prove the formula KK talks about, for general number of shields N.
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