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If Z is a compressibility factor, van der Waals equa- tion at low pressure can be written as:

$\begin{array}{1 1}(A)\;Z=1-\large\frac{Pb}{RT}\\(B)\;Z=1+\large\frac{Pb}{RT}\\(C)\;Z=1+\large\frac{RT}{Pb}\\(D)\;Z=1-\large\frac{a}{VRT}\end{array} $

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The van der Waals equation of state
$(P+\large\frac{a}{V_m^2})$$(V_m-b)=RT$
At low pressure, $V_m -b \approx V_m$ , the equation reduces to
$(P+\large\frac{a}{V_m^2})$$(V_m)=RT$
$\Rightarrow PV_m+\large\frac{a}{V_m}$$=RT$
$Z=\large\frac{PV_m}{RT}$$=1-\large\frac{a}{V_mRT}$
Hence (D) is the correct answer.
answered Apr 7, 2014 by sreemathi.v
 

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