{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

probset11

# probset11 - Physics 5524 Statistical Mechanics Problem Set...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 5524 Statistical Mechanics Problem Set 11 Due: Wednesday, Apr. 14 11.1 Problem 18, Chapter 7 of Pathria, Pg. 191. 11.2 Consider a gas of photons with dispersion ω ( ~ k ) = c | ~ k | where c is the speed of light. The photons are confined to a three-dimensional volume V and are in thermal equilibrium at temperature T . (a) For this photon gas, obtain an expression for the grand potential Σ =- k B Tln Z where Z is the grand partition function (remember that the chemical potential for photons is zero). This expression will involve an integral over frequency which you should not try to evaluate. (b) Show that the dependence of Σ on volume V and temperature T is of the form Σ ∝ V T α and determine the exponent α . (c) Show that the dependence of the entropy of this gas S on volume V and temperature T is of the form S ∝ V T β , and determine the exponent β . (d) Now assume this gas undergoes an adiabatic (i.e. Δ S = 0) expansion with initial temperature T i = 3000 K and final temperature...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

probset11 - Physics 5524 Statistical Mechanics Problem Set...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online