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