Question
The compressibility factor for a real gas at high pressure is :
A.
$$1 + \frac{{RT}}{{pb}}$$
B.
$$1$$
C.
$$1 + \frac{{pb}}{{RT}}$$
D.
$$1 - \frac{{pb}}{{RT}}$$
Answer :
$$1 + \frac{{pb}}{{RT}}$$
Solution :
$$\eqalign{
& \left( {p + \frac{a}{{{V^2}}}} \right)\left( {V - b} \right) = RT\,{\text{at}}\,{\text{high}}\,{\text{pressure}}\,\frac{a}{{{V^2}}}\,{\text{can}}\,{\text{be}}\,{\text{neglected}} \cr
& PV - Pb = RT\,\,{\text{and}}\,PV = RT + Pb \cr
& \frac{{PV}}{{RT}} = 1 + \frac{{Pb}}{{RT}} \cr
& Z = 1 + \frac{{Pb}}{{RT}};\,\,\,Z > 1\,\,{\text{at}}\,{\text{high}}\,{\text{pressure}} \cr} $$