The Third Law of Thermodynamics
If the entropy of every element in its stable state at T = 0
is taken as zero, every substance has a _ entropy
which at T = 0 may become zero, and does become zero
for all perfect _ substances, including compounds.
_ Heat T
Paul Percival
Modified by Jed Macosko
10/30/2006
Paul Percival
Modified by Jed Macosko
10/30/2006
Paul Percival
Modified by Jed Macosko
10/30/2006
Paul Percival
Modified by Jed Macosko
10/30/2006
Paul Percival
Modified by Jed Macosko
10/30/2006
Paul
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Heat Engines
A heat engine is a system capable of transforming heat into
_ by some cyclic process.
We will see that an _ cyclic process can not
produce net work. (2nd Law of Thermodynamics)
The _ of a heat engine is defined as the ratio of
the work produc
Thermochemistry
The study of energy changes that occur during chemical
_ :
at constant volume
U = qV
no _
at constant pressure
H = qP
only _ work
For practical reasons most measurements are made at
constant _, so thermochemistry mostly deals with H.
H rea
Physics 745 - Group Theory
Solution Set 26
1. [10] Below is a list of reactions that are possible. You should know the charge
and baryon number of the proton (p), electron (e) and
neutron (n). Deduce the charge Q and baryon number B
p + p +n+ p
of all lis
Physics 745 - Group Theory
Solution Set 27
1. [5] This problem has to do with demonstrating that according the isospin
symmetry, the three s all have the same mass.
(a) [2] Work out the effects of the isospin operators I on all three of the
states.
These
Physics 745 - Group Theory
Solution Set 28
1. [15] The group SU(3) contains the group SU(2) as a subgroup, and in more than
one way
(a) [7] Show that the generators T1, T2 and T3 form an SU(2) subgroup; that is,
show that [T1 , T2 ] = iT3 , etc. To save t
Physics 745 - Group Theory
Solution Set 29
1. [5] Using a weight diagram, or tensor methods (your
choice), work out the decomposition of the tensor product
3 3 into irreps.
T8
If you add the three weights to themselves, you get a total of
T3
nine possible
Physics 745 - Group Theory
Solution Set 30
1. [5] The mass of the can be predicted in terms of the parameters a and b from
eq. (4.36).
(a) [2] Find the formula for the mass in terms of a and b.
This is straightforward:
m = awijk wijk + bwijk wijl (T8 )l =
Physics 745 - Group Theory
Solution Set 25
1. [15] In the electric dipole approximation, the rate at which an atom decaying
from one state to another by the emission of a photon is given by
2
3
( I F ) = 4 IF rFI c 2 where
3
rFI = F r I
The absolute valu
Physics 745 - Group Theory
Solution Set 24
1. [5] The total angular momentum of an atom actually has three pieces: The
orbital angular momentum of the atom, the spin of the electron, and the spin of
the nucleus.
(a) [1] Suppose a hydrogen atom has a singl
Physics 745 - Group Theory
Solution Set 20
1. [10] Prove, using only the commutation relations, the first three identities (2.9)
from the notes, namely
T2 , Ta = 0,
[T3 , T ] = T ,
and T2 = TT + T32 T3
These are, in fact, three, two, and two identities r
Physics 745 - Group Theory
Solution Set 21
1. [10] In class (or the notes), I gave explicit instructions for how to find the
j
irreducible representations Ta( ) . To demonstrate that you understand this, write
2
2
2
2
explicitly T3( ) , T( ) , T1( ) , and
Physics 745 - Group Theory
Solution Set 22
1. [10] It is rare we will actually use the representation matrices ( j ) ( R ) , but
occasionally it is useful. We want to work out explicitly ( 2 ) ( R ( x ) ) , generated
1
by the generators
Ta = 1 a ,
2
0 1
Physics 745 - Group Theory
Solution Set 23
1. [20] The group SU(2) shows up in surprising places. Consider, for example, the
two-dimensional harmonic oscillators, which can be written in the form
H = ( a1 a1 + a2 a2 + 1)
where a1 and a2 are two operators
Name _
Solutions to Final Exam
March 30, 2010
This test consists of three parts. For the first part, you may write your answers directly on the
exam, if you wish. For the other parts, use separate sheets of paper. Useful equations can be
found at the star
Name _
Final Exam
March 30, 2010
This test consists of three parts. For the first part, you may write your answers directly on the
exam, if you wish. For the other parts, use separate sheets of paper. Useful equations can be
found at the start of part 3.