KQueeney's Values

From Infrared  (IR) spectroscopy  K. Queeney '92 found the following fundamental frequencies of the three normal modes of SO_2

ν_1 = 520 cm^(-1) 3 10^10cm s^(-1) ;

ν_2 = 1150 cm^(-1) 3 10^10cm s^(-1) ;

ν_3 = 1355 cm^(-1) 3 10^10cm s^(-1) ;

Some parameters

h = 6.62608  10^(-34) J s ;

k = 1.38066 10^(-23) J K^(-1) ;

R = 8.31451 J K^(-1) mol^(-1) ;

We define the following function of temperature

u[i_, T_] = (h ν_i)/(k T)

(4.79922*10^-11 K s ν_i)/T

From Statistical Mechanics we know that the contribution to the heat capacity due to the vibrational modes is given by:

Cvib[T_] := Underoverscript[∑, i = 1, arg3] (u[i, T]^2Exp[-u[i, T]])/(1 - Exp[-u[i, T]])^2R

Now, the heat capacity at two different temperatures

Cvib[298 K]

(6.5512 J)/(K mol)

Cvib[500 K]

(13.166 J)/(K mol)

For sulfur dioxide the total heat capacity is given by:

CV[T_] := 3 R + Cvib[T]

Finally the heat capacity at two different temperatures is

CV[298 K]

(31.4947 J)/(K mol)

CV[500 K]

(38.1095 J)/(K mol)

Problem 2. - Plot the specific heat from 10 K to 2000 K.

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