Question

Generalized compressibility factor chart is a plot of:

• A. Compressibility factor versus reduced temperature with reduced pressure as parameter
• B. Compressibility factor versus reduced pressure with reduced temperature as parameter
• C. Compressibility factor versus reduced pressure with absolute temperature as parameter
• D. Compressibility factor versus reduced temperature with absolute pressure as parameter

Hint:

Generalized thermodynamic charts always use reduced dimensionless properties ($P_{\text{r}}, T_{\text{r}}$) instead of absolute values ($P, T$) so that a single chart can be applied to many different gases.

Answer 1

The Correct Option is B

Concept: The compressibility factor ($Z = \frac{PV}{RT}$) measures how much a real gas deviates from ideal gas behavior ($Z=1$). According to the Principle of Corresponding States, different real gases exhibit similar volumetric behavior when their properties are scaled relative to their respective values at the critical point. These scaled coordinates are called reduced properties:

• Reduced Pressure: $P_{\text{r}} = \frac{P}{P_{\text{c}}}$

• Reduced Temperature: $T_{\text{r}} = \frac{T}{T_{\text{c}}}$

Step 1: Identify the axes of the generalized chart.
The standard Nelson-Obert generalized compressibility chart is constructed to plot the compressibility factor $Z$ on the vertical y-axis against the reduced pressure $P_{\text{r}}$ on the horizontal x-axis.

Step 2: Identify the parameter curves.
The chart displays a family of isotherms representing constant values of the reduced temperature $T_{\text{r}}$. This allows a designer to look up $Z$ for any gas given its reduced pressure and temperature coordinates. Therefore, the chart plots $Z$ versus reduced pressure ($P_{\text{r}}$) with reduced temperature ($T_{\text{r}}$) as the parameter. This matches Option B.