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Exam 2 NAME: _~ obs hous
Thermo. & Stat. Mech.
PHYS 4420, Spring 2010
In this exam, you can use a double-sided equation/formula sheet, a calculator, and an
integral table. You cannot discuss the problems with anyone, and cannot give or receive
help from anyone.
You must hand in your paper by the end of class time (9:50am) unless prior arrangements
have already been made with the instructor.
Good luck!
Problem 1:
Problem 2:
Problem 3:
Total :
Problem 1. (20pts. total)
Multiple Choice Questions, NO PARTIAL CREDIT)
You must CIRCLE the correct answer.
L.1 (4pts)
10” (distinguishable) coins are thrown on a table, What is the entropy of the system
(considering only the different H/T configurations of this fixed number of coins)?
Boltzmarin’s constant: k =1.38x10" YK.
(A) 1.38 VK
(B) 138x107 YK
(C) 1.38x10" WK iS>
(os. IK
(E) 0.96x10 YK
Ba
a}
hbase, ~ ROL. hve)
= OVE %
io
1.5 (4pts)
Estimate the Fermi temperature 7’, of the free electron gas in silver. The mass density of silver is
Pay = 10.498. , the atomic (molar) mass is Mi = 107.378 , and there is one conduction
om mol ee
(or free) electron per atom in silver.
Electron mass: m=9.1x107 kg.
Boltzmann’s constant: & = 138x107 I/K.
Planck’s c : h = 6,626x10™ Js,
anck's constant: x 8, ac fron Lites; 4 :
(A) 7, =82,000K Ny « yy = vt x x to? »
My
T, = 64,000K f
(©) 7, = 32,000K 2 5. e3he« (ah
hae
@) T, ~24,000K
2 A
() Tf, ~12,000K h %
&- 2 [oo Ae.
F~ Im, \ 97
Te Fe 64752 4
&
Problem 2. (20pts)
2
Consider a two-dimensional non-telativistic tree electron gas (€ =>) confined to an
m
area A= L’. The number of electrons is N. 7
bi Ne » Mee 43,3)...
(a) (6pts) Obtain the density of states g(e). L. i en
mt Vir au Seon S
62 DE fay
Lat au am |
he
= i, + ).
mA eon myn v
-- .
WO) btn eo ba bmA ~ LIMA ,
ad 7 ar a
9@= Gi) 20 20. ge MTNA _ IAM
h? pe
LY
(b) (6pts) Express the pepmi energy in terms of the density N/A.
gre 4) ee a
Tey, Selena = [awde - ead ae Da
veoh, G)
(c) (Apis) Find U,, the internal energy of pe system at T=0.
ire QTso
U, = [eves [oven - Pine ede -Llimd 5
ae
pelt) EO) Bae)
tyme? reo )
(d) pts) Obtain P,, the pressure of the system at T =0. Express P. in terms of the
density N/A.
C4 feecrne PL ty tlre, fee, ade 2 ( ep’)
2 . 2
Pam G)
Ab bers tue oboe! P - aoe R,. (EF
PG) » 5B -
