The ideal gas law is one example of an equation of state. It relates the pressur
ID: 1474812 • Letter: T
Question
The ideal gas law is one example of an equation of state. It relates the pressure, volume, temperature and amount of gas. Another equation of state which better models real gases is the van der Waals equation: [P+a(n/V)^2] (V - nb) = nRT. In the van der Waals equation, a and b are constants which depend on what type of gas you have. The constant "a" is determined by the strength of intermolecular forces and is quite large for water vapor compared to the noble gases. The constant "b" is determined by the size of the molecules. Larger molecules have larger values for "b". What are the SI units for "a" and "b"? Solve the van der Waals equation for P. Determine the work done on n moles of a van der Waals gas which expands isothermally at a temperature T from a volume V_1 to a volume V_2.Explanation / Answer
a)
The SI unit of a =(V/n)2[nRT/(V-nb) -P] is atm*L2/mol2
The SI unit of b =(V/n) -RT/(P+(n/V)2) is L/mol
b)
Van der Waals equation for P = nRT/(V-nb)-a(n/V)2
c)
We know that W =-integral of PdV........(1)
The expression for the P = nRT/(V-nb)-a(n/V)2
Substituting the above equation in equation (1) we get
W =-integral V1 toV2 of ( nRT/(V-nb)-a(n/V)2)dV
Separating the terms and integrating with the limits and finally we get
W =-nRTln(V2-nb/V1-nb) -an2(1/V2-1/V1)
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