In this problem we want to calculate the fugacity of saturated steam at 250 degrees C using
data from the steam tables.
So the idea would be, the steam tables have enthalpy and entropy values, so the plan would
be to calculate Gibbs free energy at saturated steam conditions.
And then we can take advantage of the relation between fugacity and Gibbs free energy.
Essentially we have to have a reference point or we know the fugacity, which would be at
the same temperature, but a low pressure.
So the idea would be to go to the steam tables, look up values.
So at 250 degrees C, the saturation pressure for steam is 3.97 mPa.
And then we can look up the values for enthalpy and entropy.
So these are the values from the steam tables for enthalpy and entropy for the vapor phase.
And this means that we can use the definitions for Gibbs free energy, H-TS, equals 2800 minus
the temperature which is 250-273.2 to make it absolute temperature times 6.07.
So this gives us the Gibbs free energy of -376 and this is Joules per gram.
Now we are going to convert because we have to work in moles for the equations that relate
Gibbs free energy to fugacity. 18 g/ mol and so the Gibbs free energy is J now per mole.
The equations that relate Gibbs free energy, and so, it says that we have the Gibbs free
energy of a component i, let's say at condition 2 minus the Gibbs free energy of component
i at condition 1, divided by RT, this is just related to the fugacity and this is how we
origionally define fugacity.
So I'm going to call, so this is for a single component that's why the i is there, and I'm
going to call this condition 2.
So we have this value.
This is what we are trying to solve for.
So we need another condition where we know the fugacity, which means at low pressure
fugacity of component that we are interested in, in this case steam, is equal to the pressure.
And we can go to the steam tables, 250 degrees C. The lowest pressure is 0.1 mPa.
And for steam at those conditions we can look up the value for H and S. So these are values
from the steam table.
I'm going to call this condition 1.
And so for steam at condition 1 I can calculate its Gibbs free energy from our definition
of G. 2977-(250+273.2)*9.10.
So the Gibbs free energy at condition 1 is -1784 J/g.
Again, 18 g/mol put it in the appropriate units for the equation, and the value is -32,112
J/mol.
So the equation that we wrote up here, we are now going to use to make the substitutions.
Gibbs free energy 2 is -6767 and then Gibbs free energy 1, -(-32112) these are both J/mol.
Gas constant, 8.314 J/mol K. Temperature, 273.2+250 K. And
this is the log of fugacity of component steam condition 2 over fugacity condition 1.
But the fugacity at condition 1 is 0.1 mPa because this is the pressure.
Ideal gas at the low pressure where we calculated the fugacity or the Gibbs free energy.
So low enough pressure, ideal gas fugacity and pressure are the same.
So the left side of the equation we can then calculate and 5.8 is equal to this log of
the fugacity ratios.
So the fugacity at condition we are interested in is 3.
4 mPa.
So this is fugacity at a pressure of saturation pressure, from the steam tables, is 3.97.
So at 250 C, 3.97 mPa, fugacity, this is steam, is equal to 3.4 mPa.
So a reasonable check is fugacity is less than the pressure, which is typically what
we expect.
It's a similar value, so steam is non ideal at 250 C and 3.97 mPa.