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