Question Details

(Solution) - Gruneisen constant a Show that the free energy of a phonon

Brief item decscription

Solution download


Item details:

Gruneisen constant

 

(a) Show that the free energy of a phonon mode of frequency w is kBT in [2sinh (hw/2kBT)]. It is necessary to retain the zero-point energy ½hw to obtain this result.

 

(b) If ? is the fractional volume change, then the free energy of the crystal may be written as F(?, T) = ½ B?2 + kBT ? In [2sinh (hwK/2kBT)] where B is the hulk modulus. Assume that the volume dependence of wK is ?w/w = ???, where ? is known as the Gruneisen constant. If ? is taken as independent of the mode K, show that F is a minimum with respect to ? when B ? = ??1/2hw coth (hw/2kBT), and show that this may be written in terms of the thermal energy density as ? = ?U(T)/B.

 

(c) Show that on the Debye model ? = ? ? In ?/? In V. Note: Many approximations are involved in this theory: the result (a) is valid only if w is independent of temperature; ? may he quite different for different modes.

 







About this question:
STATUS
Answered
QUALITY
Approved
ANSWER RATING

This question was answered on: Jul 11, 2017

PRICE: $15

Solution~000909728067.zip (18.37 KB)

Buy this answer for only: $15

Pay using PayPal (No PayPal account Required) or your credit card. All your purchases are securely protected by PayPal.
SiteLock

Need a similar solution fast, written anew from scratch? Place your own custom order

We have top-notch tutors who can help you with your essay at a reasonable cost and then you can simply use that essay as a template to build your own arguments. This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student. New solution orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below.

Order Now
v>