Equipartition of Energy
The energy of a molecule is equally divided among all types of
motion or degrees of freedom
For 1 mole of a diatomic gas:
U = 3 RT + RT + RT = 7 RT
2
2
molar internal energy = translation + rotation + vibration
1
It is easier to excite a molecule to a higher rotational level than to a higher
vibrational or electronic energy level.
The ratio of the population in any two energy levels E2 and E1 is given by
the Boltzmann distribution law
N2
= e − ∆E k BT
N1
The number of the molecules in the upper level are always less than in the
lower level
2
 ∂U 
Molar heat capactity: C V = CV / n and CV =  ∂T 

V
 3

 ∂ ( RT ) 
3
2
 = R = 12.47 JK −1mol −1
C
v =
For 1 mole of monoaromic gas:
2
 ∂T 



V
 7

 ∂ ( RT ) 
7
2
 = R = 29.10 JK −1mol −1
C
v =
For 1 mole of diatomic gas:
2
 ∂T 



V
If we neglect the vibrational part then
and
U = 3 RT + RT = 5 RT
2
2
 5

 ∂ ( RT ) 
5
 = R = 20.79 JK −1mol −1
Cv =  2
for a diatomic gas
2
 ∂T 



V
3
4