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Reduced Properties

First, we need a way to quantify exactly how close a given state is to the critical state.

We accomplish this by defining three reduced properties.

Knowing Tc, Pc, and

, the following dimensionless reduced properties can be determined :

Reduced

Temperature

, TR:

Reduced
Pressure

, PR:

Ideal Reduced Molar Volume

Remember that the subscript "C" referes to properties at the critical state and properties without a subscript refer to properties at the real state in which you are interested.

Lesson 2E: page 9 of 13

Ch2, Lesson E, Page 9 - Reduced Properties

The first step in determining a good estimate of the molar volume at a given temperature and pressure is to determine exactly how close the given state is to the critical point.
We use reduced properties to help us quantify how close is close.
Reduced temperature pressure and ideal molar volume can be calculated using the equations shown here.
The reduced ideal molar volume is just the molar volume that the gas WOULD have at its critical point IF it were an ideal gas.
Notice that the reduced properties all have a value of 1 at the critical point. In general the values of the reduced properties fall between zero and 5 and are often between 0.5 and 2.
So far, I have used an example in which the temperature and pressure are known and the molar volume is the unknown we wish to estimate.
But, just as if we were using the ideal gas EOS, this method allows us to calculate any one of these 3 reduced properties given values for the other 2.
But what do we do with this reduced property once we have determined a value for it ?
Well, we just solve one of these 3 equations for the real unknown property, whether its T, P or molar volume and we are done !
So, now the problem has become determining one unknown reduced property given the other 2.
Let’s see how we are going to do that.

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