The discussion revolves around obtaining the chemical potential of water using the Van der Waals model, specifically as a function of temperature and volume. Participants are exploring the relationship between chemical potential and Gibbs free energy.
Participants are actively engaging with the problem, with some providing relationships and equations relevant to Gibbs free energy and chemical potential. There is a mix of understanding and uncertainty, with guidance being offered on how to approach the calculations and relationships involved.
Participants are referencing textbook material and specific equations, indicating a reliance on established thermodynamic principles. The discussion includes assumptions about ideal gas behavior and the conditions under which the calculations are being made.
So, if you could calculate the gibbs free energy per mole as a function of temperature and volume for a van der walls gas, you would have your answer. Suppose you took the starting state of g = 0 as water vapor at 25 C and the corresponding equilibrium vapor pressure (i.e., in the ideal gas region). Could you determine g at the same pressure and a higher temperature T (i.e., within the ideal gas region)?It's me said:By this relationship: $$\mu= \frac{G}{n}$$
Well, you need to go back to your textbook and find out how to determine that change in free energy with temperature at constant pressure.It's me said:I'm sorry I don't understand how I could determine that.
No. The number of moles should also be held constant.It's me said:It is this relation? $$dG=-SdT+\mu dn$$
Good. So, if we rearrange this, we get:It's me said:$$G=H-ST$$ $$S=\frac{H-G}{T}$$ $$dG=-SdT$$ $$\rightarrow dG=-(\frac{H-G}{T})dT$$