THERMO4

Question 1

What is cv’ ?

Answer 1

molar specific heat, the energy required to raise the temperature of one mole of a substance by 1K

Question 2

What are the three types of degrees of freedom?

Answer 2

• translational
• rotational
• vibration

Question 3

Degrees of Freedom

Translation

Answer 3

-3 possible degrees if freedom, one in each direction x, y and z
1/2mVav² = 1/2mvx²+1/2mvy²+1/2mvz²

Question 4

Degrees of Freedom

Rotation

Answer 4

-3 possible degrees of freedom in each direction x, y and z

1/2Iω = 1/2Ixωx² + 1/2Iyωy² + 1/2Izωz²

Question 5

Degrees of Freedom
Rotation
Polyatomic vs Diatomic Gas

Answer 5

• a polyatomic gas has three rotational degrees of freedom whereas a diatomic gas has two rotational degrees of freedom
• this is because in a diatomic gas, rotation about the bond is so small that it can be ignored

Question 6

Degrees of Freedom

Vibration

Answer 6

-2 possible degrees of freedom per bond, only considered at very high temperatures
Evib = KEvib + PEvib
Evib = 1/2μv² + 1/2kx²

Question 7

Monatomic Gas

Molar Specific Heat

Answer 7

cv’ ≈ 1.5R

Question 8

Diatomic Gas

Molar Specific Heat

Answer 8

cv’ ≈ 2.5R

Question 9

Polyatomic Gas

Molar Specific Heat

Answer 9

cv’ > 2.5R

Question 10

Equipartition Theorem

Answer 10

-when a substance is in thermal equilibrium there is an average energy of 1.2kT per molecule (1/2RT per mole) associated with each degree of freedom

Question 11

Monatomic Gas

Number of Degrees of Freedom

Answer 11

3

Question 12

Diatomic Gas

Number of Degrees of Freedom

Answer 12

5

Question 13

Polyatomic Gas

Number of Degrees of Freedom

Answer 13

6

Question 14

Monatomic Gas

Eint per mole

Answer 14

3/2 RT

Question 15

Diatomic Gas

Eint per mole

Answer 15

5/2 R

Question 16

Polyatomic Gas

Eint per mole

Answer 16

3 RT

Question 17

Failure of the Equipartition Theorem

Answer 17

• molar heat capacity changes with temperature as the number of degrees of freedom changes with temperature
• gaps between translational energy levels are very small, between vibrational energy levels are slightly bigger and between vibrational energy levels much bigger
• molecules have to transition completely between energy levels, they can’t move half way
• molecules typically share E=kT during in a collision
• if kT

Question 18

Crystalline Solids

Vibration of Atoms

Answer 18

-each atom in a crystalline solid can vibrate about its equilibrium position

Question 19

Dulong Petit Law

Answer 19

cv’ = 3R

for all solids, valid at high temperatures