Question

At low pressures, van der Waal's equation is written as $(P+\frac{a}{V^2})V=RT$. The compressibility factor is then equal to:

• A. $(1-\frac{a}{RTV})$
• B. $(1-\frac{RTV}{a})$
• C. $(1+\frac{a}{RTV})$
• D. $(1+\frac{RTV}{a})$

Answer 1

Answer: (A)

$(1-\frac{a}{RTV})$

$\left[P+\frac{a}{V^2}\right][V-b]=RT$

At low pressure,volume correction left b right may be neglected.

Thus,

$\left[P+\frac{a}{V^2}\right][V-b]=RT$

Or

$PV+\frac{a}{V}=RT$

Or

$PV=RT\left[1-\frac{a}{RTV}\right]$