Compressibility Factor and Generalized Compressibility Chart

From my understanding, the compressibility factor is defined by

$$Z=\frac{pv}{RT}=\frac{p\bar{v}}{\bar{R}T}$$

It can also be defined by the ratio of the real molar volume of a gas to the ideal molar volume of a gas at the same temperature and pressure. Essentially it corrects for the deviation of a real gas from an ideal gas.

On a generalized compressibility chart, the compressibility $$Z$$ is plotted as a function $$f=f(p_R,T_R)$$ of the reduced pressure and temperature. I don't understand why exactly; it would be nice if someone could explain that a little more.

Another thing I'm confused about is the psuedoreduced specific volume, given by

$$v'_{R}=\frac{\bar{v}}{\bar{R}T_c/p_c}$$

Why don't we use the reduced specific volume as opposed to the psuedoreduced specific volume?

In my thermodynamics class, I was presented with the following question:

Determine the temperature, in °C, of air at 30 bar and a specific volume of 0.013 $$m^3/kg$$. Use compressibility chart.

I was confused about how to figure out this problem since I can't find the reduced temperature without the actual temperature of the air.

• This is a trial and error calculation. Mar 1 at 22:08
• @ChetMiller How so? Is there not one answer? Mar 1 at 22:30
• There is one answer. Do you know what a trial and error calculation is? Mar 1 at 22:31