If Z is a compressibility factor, v...
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If ( Z ) is a compressibility factor, van der Waals' equation at low pressure can be written as
(a) ( quad Z=1+frac{R T}{p b} )
(b) ( Z=1-frac{a}{V R T} )
(c) ( quad Z=1-frac{p b}{R T} )
(d) ( Z=1+frac{p b}{R T} )

11th - 12th Class
Chemistry
Solution
1327
Rating
2.4 (10 ratings)
If Z is a compressibility factor, van der Waals' equation at low pressure can be written as
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Van der Waals equation is given by
[
left(rho+frac{a}{V^{2}}right)(V-b)=R T
]
At low pressure, ( V ) decreases. Thus, ( frac{a}{V^{2}} ) increases. However, ( V ) is still large enough is comparison to ( b ) hence ( b ) can be neglected. Thus, van der Waals' equation becomes
[
left(rho+frac{a}{V^{2}}right) V=R T
]
( Rightarrow quad rho V+frac{a}{V}=R T )
( Rightarrow quad rho V=R T-frac{a}{V} )
( Rightarrow quad frac{rho V}{R T}=1-frac{a}{R T V} )
( Z=1-frac{a}{R T V} quadleft[because frac{rho V}{R T}=Zright] )

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