Example 2.4 A gas follows van der Waals equation of state.  Calculate its specific volume at 78.95 atm and 100 °K.   The following data are provided.  a = 1.39 L2·atm/mol2 , b = 0.03913 L

 

Solution 

Number of moles, n = 1

Van der Waals equation of state (Equation 2.8):

$                 Function F(V) (Equation 2.11):

$                 Derivative F'(V) (Equation 2.12):

 

$                 Initial guess, V0 (Equation 2.1):

$                 Vi (Equation 2.13)

 

i

 

Vi

 

F(Vi)

 

F'(Vi)

 

Vi + 1

 

0

 

0.104

 

0.057

 

1.601

 

0.069

 

1

 

0.069

 

0.103

 

0.954

 

0.055

 

2

 

0.055

 

7.36 ´ 10-4

 

0.863

 

0.054

 

3

 

0.054

 

1.15 ´ 10-6

 

0.86

 

0.054

 

Specific volume, V = 0.054 L/mol.