Question

Thermodynamics:

What is the significance of:

a reduced pressure and reduced temperature of 1, and;

a compressibility factor (Z) of 1?

At room temperature, what pressure is needed in order to say that nitrogen is non-ideal if you define non-ideal as 5% error from the ideal gas law?

Answer 1

The reduced state of a gas corresponds to a state where Pr = P/Pc that is the ratio of pressure to its critical pressure, Vr = V/Vc and Tr = T/Tc.

Ususally the reduced state or corresponding state is considered from the temperature.

The boiling point of a liquid is about 2/3 of its critical temperature in absolute scale. The boiling temperature is regarded as the corresponding temperature and the law of corresponding state is valid at boiling point of liquids.

the law of corresponding states is

{Pr +3/Vr²} {3Vr-1} = 8Tr

When reduced pressure and temperautre are stated as unity , it means it is at the critical state not at its boiling point.

2) compressibility factor of 1 means the molar volume of gas when it is behaving ideal and real are same.

   z, the compressibility factor is defined as the ratio between molar volume of gas when it is ideal to real.

     Z = Vm(ideal)/ Vm(real)

3) If there is 5% error from ideal gas law, according to ideal gas the pressure of one mole of gas at standard temperature of zero Celsius should be one atmosphere or 760 mmHg.

If it has 5% error, it can be 760 + or - 38 mmHg