Question

If $\left(\frac{ab}{V^2}\right)$ is negligible, then second virial coefficient B in virial equation is?

• A. $(b-\frac{a}{RT})$
• B. $(b+\frac{a}{RT})$
• C. $(b+\frac{a}{RTV})$
• D. $(b-\frac{a}{RTV})$

Answer 1

Answer: (A)

$(b-\frac{a}{RT})$

The virial equation:

Now Van der Waal's equation of real gas:

$(P+\frac{a}{v^2})(v-b)=RT$

$\Rightarrow (PV+\frac{a}{v})=RT{(1-\frac{b}{v})}^{-1}$

$=RT[1+\frac{b}{v}+\frac{b^2}{v^2}+\frac{b^3}{v^3}...](\frac{b}{v}<1)$

$\Rightarrow PV=RT[1+\frac{1}{v}(-\frac{a}{RT}+b)+\frac{b^2}{v^2}+\frac{b^3}{v^3}...]$

$\therefore B=b-\frac{a}{RT}$