MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01T
Fall Term 2004
Practice Exam Three Solutions
Problem 1a) (5 points) Collisions and Center of Mass Reference Frame
In the lab frame, Cart A is at rest. An identical cart B, of the sa
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Practice Exam #2
Problem 1 (35 points) Weakly Interacting Bose Gas
At low temperatures the entropy and isothermal compressibility of a weakly interacting
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions, Practice Exam #2
Problem 1 (35 points) Weakly Interacting Bose Gas
@P
@P
a)
dP =
dT +
dV
@T V
@V T
@P
=
2cV 3 from given
@V T
@P
@S
5
=
= aT 3
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #9
Problem 1: The Big Bang
If the expansion is adiabatic,
S = 0.
S =
@F
@T
@
@T
=
V
1 2
(kT )4 V
3 ~3
45 c
4 2 4 3
k T V
45 c3 ~
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #8
Due in hand-in box by 12:40 PM, Wednesday, April 10
Problem 1: Dust Grains in Space
Astronomers have discovered that there exist in the in
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #9
Due in hand-in box by 4;00 PM, Friday, April 19
Problem 1: The Big Bang
Early in the evolution of the universe, when the universe occupied
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'3 vec(k) cfw_3 U' amt
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11*: \1W\ U 1 ("m [3%
IV: ~31) NC 23 MO A
N30
11 t M AX a=1im
x Mao Ec % Ail->0 A
Louvd +nam5onmJK cfw_on
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #8
Problem 1: Dust Grains in Space
a) H is separable: the 6 variables are statistically independent.
p(1 , 2 , 3 , L1 , L2 , L3