p=pressure of the gas 
                    V=real volume of the gas
                    R=universal gas constant
                    T=absolute temperature

My question is that whether p is real pressure of the gas or ideal pressure of the gas...It is mentioned nowhere..If it is real pressure than we cannot apply ideal gas equation and cannot write Z=Vreal/Videal..but in actual compressibility factor is also defined as the ratio of real volume of gas /ideal volume of gas..How it is derived.And please mention whether p is considered as ideal pressure or real pressure....

  • $\begingroup$ P is pressure, both real and ideal. With the Z-equation, we are comparing volumes of RG and IG kept at the same P,T. Of course, it will give the answer for real pressure if you substitute measured volume and temperature. Note that Z can be the.same f or multiple values of P, but usually not for V. $\endgroup$ Feb 27, 2012 at 3:48
  • $\begingroup$ ok you mean that compressibility factor is the way of comparing real and ideal gases kept at same temp and pressure...please comment whether i have interptetted it well..please can you elucidate your last line also? ...your answer helped me a lot.thnx...and please do these two things.. $\endgroup$
    – Manisha
    Feb 27, 2012 at 4:18
  • $\begingroup$ Replied as an answer; too long for comments. $\endgroup$ Feb 27, 2012 at 8:55

1 Answer 1


Yes, the CF is a way of comparing RGs and IGs kept at same temperature and pressure. It is a comparison of volumes, as stated in the question. Hence the name "compressibility factor".

The CF equation can be better stated as: $P_{obs}V_{m,obs}=ZRT_{obs}$, where the m stands for "molar", and "obs" means "observed". This is in contrast with $P_{obs}V_{m,expected}=RT_{obs}$, the real gas equation.

We can write the real gas equation in this form as well, changing the identity of the observed values: $P_{expected}V_{m,obs}=RT_{obs}$. Here what I did was I decided to measure T and V instead, and "expect" a value for P. We can do the same thing for T.

Basically your confusion is in the fact that "real" and "ideal ("observed" and "expected") values are not well defined. The "real" value will be the "ideal" value for two out of the three variables. We can choose to "observe" two variables, and "expect" the third by ideal gas law, or we can "observe" the third as well by applying compressibility factor and verifying. Here, the variable you are trying to determine is volume, so "real pressure" is "ideal" pressure

What I mentioned in the comments about CF being the same for two pressures comes from this: .

Yes, it's in Italian, but basically it relates Z(y-axis), reduced pressure (x-axis), and reduced temperature (the T markings on each curve).

From here, it is obvious that, for different values of T or P, it is possible to have different values of Z. One should be careful about this while calculating stuff, that's all.

  • $\begingroup$ what i needed i got it...your comment was sufficient for me..thanx $\endgroup$
    – Manisha
    Feb 27, 2012 at 10:41

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