Question

Which of the following expressions of compression factor, $Z(=\frac{P{V}_m}{RT})$ of a real gas is applicable at high pressure?

• A. $Z=1-\frac{a}{V_{m}RT}$
• B. $Z=1+\frac{a}{V_{m}RT}$
• C. $Z=1+\frac{Pb}{RT}$
• D. $Z=1-\frac{Pb}{RT}$

Answer 1

Answer: (C)

$Z=1+\frac{Pb}{RT}$

At high pressure, pressure correction is negligible.
$P_{realgas}=P$

$P(V_m-b)=RT$

Now, $Z=\frac{P{V}_m}{RT}$

Putting $P{V}_m=RT+Pb$,

We get, $Z$ $=$ $\frac{RT+Pb}{RT}$ $=$ $1+\frac{Pb}{RT}$

(Note that $Z>1$)

Hence, the correct answer is option $\text{C}$.