Answered: al harmonic oscilla a heat bath | bartleby

Related questions

Question

One-dimensional harmonic oscillators in
equilibrium with a heat bath
(a) Calculate the specific heat of the one-dimensional
harmonic oscillator as a function of temperature
(b) Plot the T -dependence of the mean energy per
particle E/N and the specific heat c. Show that E/N →
kT at high temperatures for which kT > hw
In this limit the energy kT is large in comparison to hw
, the separation between energy levels. Hint: expand
the exponential function
1
ē = ħw
+
eBhw

(c) Show that at low temperatures for which ħu> kT ,
E|N :
= ħw(}+e-8hw)
What is the value of the heat capacity?
Why is the latter so much smaller than it is in the high
temperature limit?
Why is this behavior different from that of a two-state
system?
(d) Verify that S>0 as T→O in agreement with the
third law of thermodynamics, and that at high T,
S> kN In(kT /hw).

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Plz solve all parts
12
A particle vibrated at a frequency of 100 hz and a amplitude of 0.03 cm Calculate speed and particle acceleration at Max junction. Specify the position of particles as a function of time!
Consider a which m" ů O•os hq and 'k is 5ONm. State and sketch the nature f oscillatog. motion when the damping Constant b is )0.1N - s/m li) L-ON-5/m and SN-5/m. damped hamardk osallator der
Question 1: By what factor should the length of a simple pendulum be changed in order to triple the period of vibration? O 3 27
Imagine a bar of gold is hung on a spring in your kitchen and it extends the spring by 7 cm. At approximately what frequency in Hz (cycles per second) wilI the bar oscillate up and down when given a gentle vertical kick, if there is essentially no damping. Hz If we take the spring and the bar of gold to the surface of the moon, will the oscillation frequency there be higher, lower, or the same? Explain your answer above.
T14f, please help me with my reviewer, I can’t get the answer for the step 2.
What is the period of oscillation of a liquid contained in a U tube executing simple harmonic motion?
A grandfather clock uses a brass pendulum to keep perfect time at room temperature. If the air conditioning breaks down on a very hot summer day, how will the grandfather clock be affected? Explain your answer.