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Flashcards in THERMO4 Deck (19):
1

What is cv' ?

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

2

What are the three types of degrees of freedom?

-translational
-rotational
-vibration

3

Degrees of Freedom
Translation

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

4

Degrees of Freedom
Rotation

-3 possible degrees of freedom in each direction x, y and z
1/2Iω = 1/2Ixωx² + 1/2Iyωy² + 1/2Izωz²

5

Degrees of Freedom
Rotation
Polyatomic vs Diatomic Gas

-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

6

Degrees of Freedom
Vibration

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

7

Monatomic Gas
Molar Specific Heat

cv' ≈ 1.5R

8

Diatomic Gas
Molar Specific Heat

cv' ≈ 2.5R

9

Polyatomic Gas
Molar Specific Heat

cv' > 2.5R

10

Equipartition Theorem

-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

11

Monatomic Gas
Number of Degrees of Freedom

3

12

Diatomic Gas
Number of Degrees of Freedom

5

13

Polyatomic Gas
Number of Degrees of Freedom

6

14

Monatomic Gas
Eint per mole

3/2 RT

15

Diatomic Gas
Eint per mole

5/2 R

16

Polyatomic Gas
Eint per mole

3 RT

17

Failure of the Equipartition Theorem

-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

18

Crystalline Solids
Vibration of Atoms

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

19

Dulong Petit Law

cv' = 3R
for all solids, valid at high temperatures