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Thermal & Kinetic Lecture 10
Revision I: Problems and Previous Exam. Questions
I would prefer to have the slides available from the website before the lecture.
a) Yes
b) No
c) Don’t care
Equipartition and
Specific Heats
Thermal & Kinetic paper, ’06/’07: Q1
For this question,
I don’t
know
wher
e t..
.
I co
uld h
ave
a go b
ut I..
I am
conf
iden
t that
I ...
13%24%
63%a) I don’t know where to
begin
b) I could have a go but I’m not sure
c) I am confident that I can do it
The value of CV expected if all degrees of freedom contribute is:
24.
93 J
K-1
12.
46 J
K-1
29.
08 J
K-1
None
of the
se
11% 11%
53%
24%
a) 24.93 JK-1
b) 12.46 JK-1
c) 29.08 JK-1
d) None of these
Thermal & Kinetic paper, ’02/’03: Paper 2, Q1
Vibrational effects…
Won
’t co
ntribu
te
Will
contri
bute
Don’t
know
63%
33%
4%
1. Won’t contribute
2. Will contribute
3. Don’t know
(b) (i) kT at room temperature ~ 0.025 eV. Spacing of vibrational levels ~ 1 order of magnitude greater than this – vibrational contribution will be negligible.
At what temperature will the population of the first excited vibrational level be a factor of ten greater than the number of molecules in the second vibrational level?
512
K
136
1 K
77
K
211
2 K
9%0%3%
88%a) 512 K
b) 1361 K
c) 77 K
d) 2112 K
)exp(1
2
kT
E
N
N (b) (ii) ln (10)=0.27 x 1.6 x 10-19/(1.38 x 10-23 x T) [1] T =
1361 K [1]
(b)(iii) Consider independent degrees of freedom of diatomic molecule: 3 translation, 2 vibration, 2 rotation [1].
Each degree of freedom contributes ½ kT in energy, hence Cv = 7k/ 2 (7R/2 for 1 mole) [1] Only have 3 degrees of freedom for monatomic gas, so Cv = 3k/2 (3R/2 for 1 mole) [1]
Thermal & Kinetic paper, ’05/’06: Q3
For this question,
I don’t
know
wher
e t..
.
I co
uld h
ave
a go b
ut I..
I am
conf
iden
t that
I ...
20%11%
70%a) I don’t know where to begin
b) I could have a go but I’m not sure
c) I am confident that I can do it
If the spacing of the rotational energy levels for a certain diatomic molecule is 0.05 eV, would you expect that rotational effects will make a strong contribution to the specific heat of the molecule at a temperature of 4K?What is the heat capacity of the molecule at 4K assuming that both vibrational and rotational motion are ‘frozen out’ at this temperature?
Specific heats and equipartition of energy
Thermal & Kinetic paper, ’03/’04: Section B Q8
NB You should attempt the remainder of Q8 from the
2004 Thermal & Kinetic paper.
Boltzmann distribution
Thermal & Kinetic paper, ’06/’07: Paper 2, Q1
The dimensions of k are:
MLT-
2q
ML2T
-1q2
ML2T
-2q-1
Don’t
know
0% 0%0%0%
a) MLT-2b) ML2T-1
c) ML2T-2
d) Don’t know
Velocity and speed (Maxwell-Boltzmann) distributions
Thermal & Kinetic paper, ’04/’05: Section B Q7
Formulae given
For this question,
I don’t
know
wher
e t..
.
I co
uld h
ave
a go b
ut I..
I am
conf
iden
t that
I ...
0% 0%0%
a) I don’t know where to begin
b) I could have a go but I’m not sure
c) I am confident that I can do it