PHYS 427_HE02_A_ClosedBook_Solutions

PHYS 427_HE02_A_ClosedBook_Solutions - PHYS 427 2nd Midterm...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: PHYS 427 2nd Midterm Exam‐Part A Solutions Fall 2008 PHYS 427 Thermal and Statistical Physics 2nd Midterm Exam-Part A Solutions Zuanyi Li Problem 1 The occupied density of orbitals is the product of the density of states D3 (ε ) and the Fermi distribution function f (ε ) . Its curves for both T=0 and T finite is shown below: Density of orbitals T=0 T is finite μ 0.0 0.5 ε/εF 1.0 1.5 Problem 2 The P-V diagram for a Carnot cycle is shown below: Where A and C are isothermal processes with temperature τ h , τ l , respectively; B and D are isentropic processes. 1 / 2 PHYS 427 2nd Midterm Exam‐Part A Solutions Fall 2008 Problem 3 One should not try to invent a perpetual motion machine of the second kind because it violates the second law of thermodynamics: “It is impossible for any cyclic process to occur whose sole effect is the extraction of heat from a reservoir and the performance of an equivalent amount of work”. Be specific, entropy ( σ h = Qh / τ h ) enters the system when it extracts heat ( Qh ) from a reservoir, and this entropy must ultimately be removed from the system because an ideal device or machine need to operate in a reversible cycle. However, work does not carry entropy. To prevent the accumulation of entropy there must be some output heat ( Ql = σ lτ l = σ hτ l = Qh (τ l / τ h ) ) to remove this entropy. Therefore, heat cannot be completely converted into work. Problem 4 dF = μ dN − σ dτ − PdV dG = μ dN − σ dτ + VdP F is useful to a system at constant volume, e.g., heating a box of gas. G is useful to a system at constant pressure, e.g., chemical reactions. Problem 5 FN is approximately independent of a magnetic field Ba while FS ∝ Ba2 . 2.5 2.0 Free energy density Fs 1.5 1.0 FN Bac 0.5 0.0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Ba/Bac 2 / 2 ...
View Full Document

This note was uploaded on 12/06/2009 for the course PHYS 427 taught by Professor Flynn during the Fall '08 term at University of Illinois, Urbana Champaign.

Ask a homework question - tutors are online