# Air Compressibility Factor Calculation â€“ Sample Problem

### Problem Statement

Calculate the compressibility factor (Z factor) for air at the following temperature and pressure condition -
P = 15 barg
T = 600C

### Solution

The compressibility factor or Z factor for air is calculated in following simple steps using linear interpolation technique and air compressibility factor table.

### Step1

Temperature and Pressure unit conversion to 'Kelvin' and 'bara'.
T = 600C = 60+273.16 K = 333.16 K
P = 15 barg = 15 + atmospheric pressure = 15 + 1.013 bara
P = 16.013 bara â‰ˆ 16 bara (roughly for purpose of this calculation)

### Step2

Refer to EnggCyclopedia's air compressibility factor table to get air compressibility factors at neighboring temperature and pressure conditions. Air compressibility at following four points is noted.

 P(bara) P(bara) Air Compressibility (Z factor) 10 300 0.9974 10 350 1.0004 20 300 0.9950 20 350 1.0014

### Step3

First, mean air compressibility is calculated @ 10 and 20 bara by linear interpolation around the temperature values.

Z1 (@10bara & 333.16K) = 0.9974Ã—(350.0-333.16)/(350-300)+1.0004Ã—(333.16-300.0)/(350-300)

Z1 (@10bara & 333.16K) = 0.9974Ã—0.3368+1.0004Ã—0.6632= 0.9994

Similarly,
Z2 (@20bara & 333.16K) = 0.9950Ã—0.33680+1.0014Ã—.6632 = 0.9992

Then the air compressibility at given temperature and pressure conditions is estimated by linear interpolation around the pressure values.

Z (@16bara & 333.16K) = 0.9994Ã—(20-16)/(20-10)+0.9992Ã—(16-10)/(20-10)

Z (@16bara & 333.16K) = 0.9993

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