# Chapter 6 : Calculation of energy and heat capcity¶

## Example 6.1 Page No : 105¶

In [1]:
# Variables
import math
m = 5.313*10**-23 			#g
k = 1.38*10**-16
T = 298 			#K
R = 82.06 			#ml-atm /mol K
h = 6.624*10**-27 			#J /mol

# Calculations
Qt = (2*math.pi*m*k*T)**1.5*R*T/h**3

# Results
print  'Qt  = %.2e '%(Qt)
Qt  = 4.28e+30

## Example 6.2 Page No : 107¶

In [2]:
# Variables
import math
Qe = 4.029
Qe1 = -37.02
Qe2 = 4.695*10**4
T = 300 			#K
R = 1.98 			#cal /mol K
Qe3 = 4.158
Qe4 = -200.8
Qe5 = 2.546*10**5
T1 = 500 			#K

# Calculations
Ce = R*((Qe2/Qe)-(Qe1/Qe)**2)/T**2
Ce1 = R*((Qe5/Qe3)-(Qe4/Qe3)**2)/T1**2

# Results
print  'electronic contribution  = %.3f cal deg**-1.g.atom**-1'%(Ce)
print  ' electronic contribution  = %.3f cal deg**-1.g.atom**-1'%(Ce1)
electronic contribution  = 0.255 cal deg**-1.g.atom**-1
electronic contribution  = 0.466 cal deg**-1.g.atom**-1

## Example 6.3 Page No : 111¶

In [5]:
# Variables
import math
I = 0.459*10**-40 			#g cm**2
k = 1.38*10**-16
T = 300 			#K
h = 6.624*10**-27 			#J/mol
I1 = 245*10**-40 			# g cm**2

# Calculations
Qr = I*k*T*8*math.pi**2*0.5/h**2
Qr1 = I1*k*T*8*math.pi**2/h**2

# Results
print  'Rotational Partition  = %.2f '%(Qr)
print  ' Rotational Partition  = %.f '%(Qr1)

# note : rounding off error. please check.
Rotational Partition  = 1.71
Rotational Partition  = 1825

## Example 6.4 Page No : 114¶

In [4]:
# Variables
import math
h = 1.439
T = 300. 			#K
w = 4405. 			#cm**-1
w1 = 565. 			#cm**-1

# Calculations
Qv1 = (1-math.e**(-h*w/T))**-1
Qv2 = (1-math.e**(-h*w1/T))**-1

# Results
print  'Vibrational Partition  = %.3f '%(Qv1)
print  ' Vibrational Partition  = %.3f '%(Qv2)
Vibrational Partition  = 1.000
Vibrational Partition  = 1.071

### Example 6.5 Page No : 116¶

In [5]:
# Variables
h = 1.439
T = 300 			#K
w = 565 			#cm**-1
R = 1.98 			#cal /mol K
n = 0.56

# Calculations
Qr = h*w/T
Cv = n*R

# Results
print  'Vibrational Partition  = %.2f '%(Qr)
print  ' Cv  = %.2f cal deg**-1 mole**-1'%(Cv)
Vibrational Partition  = 2.71
Cv  = 1.11 cal deg**-1 mole**-1

## Example 6.6 Page No : 118¶

In [6]:
# Variables
R = 1.986 			#cal deg**-1 mole**-1
cv1 = 0.392 			#cal deg**-1 mole**-1
cv2 = 0.004 			#cal deg**-1 mole**-1
cv3 = 0.003 			#cal deg**-1 mole**-1
cv4 = 1.265 			#cal deg**-1 mole**-1
cv5 = 0.247 			#cal deg**-1 mole**-1
cv6 = 0.225 			#cal deg**-1 mole**-1

# Calculations
Cv  = 3*R+cv1+cv2+cv3
Cv1 = 3*R+cv4+cv5+cv6

# Results
print  'Total heat capacity  = %.2f cal deg**-1 mole**-1'%(Cv)
print  ' Total heat capacity  = %.2f cal deg**-1 mole**-1'%(Cv1)
Total heat capacity  = 6.36 cal deg**-1 mole**-1
Total heat capacity  = 7.69 cal deg**-1 mole**-1

## Example 6.7 Page No : 123¶

In [7]:
# Variables
R = 1.98 			#cal/mol K

# Calculations
Cv = 2.856*R

# Results
print  'Cv  = %.2f cal deg**-1 g.atom**-1'%(Cv)
Cv  = 5.65 cal deg**-1 g.atom**-1

## Example 6.8 Page No : 124¶

In [8]:
# Variables
R = 1.98 			#cal/mol K
n = 3

# Calculations
Cv = n*R*0.8673

# Results
print  'Cv  = %.2f cal deg**-1 g.atom**-1'%(Cv)
Cv  = 5.15 cal deg**-1 g.atom**-1

## Example 6.9 Page No : 125¶

In [9]:
# Variables
R = 1.98 			#cal/mol K
n = 3

# Calculations
Cv = n*R*0.904

# Results
print  'Cv  = %.2f cal deg**-1.g.atom**-1'%(Cv)
Cv  = 5.37 cal deg**-1.g.atom**-1
In [ ]: