# Conversion of ideal gas to real gas via $Z$ compression factor

The ideal gas equation $PV=nRT$ can be converted into real gas equation by compression factor $Z$ i.e $PV=Z~ nRT)$. My question is what is $Z$ and how does it arise? Is $PV/nRT$ a compression ratio of any gas? How does $Z$ adjust the ideal gas assumptions and allow for calculations with a real gas?

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You can define $Z$ phenomenologically as follows: calculate the ratio $PV/(nRT)$ for each PV. Call the ratio as a function of $PV$ the compression ratio, and assume it's independent of temperature and mole number. Then $PV=Z(nRT)$.
@kiranadhikari Is the problem that you're trying to interpret $Z$ as a compression ratio like the kind defined for engines? These quantities have nothing to do with one another. You can tell this, because you can compress an ideal gas, e.g. to $V^\prime = V/2$, which would give a "compression ratio" of 2, but still have Z=1 in your notation, as long as the gas is still well described as an ideal gas. –  Douglas B. Staple Apr 19 '13 at 14:45