Free energy in the free expansion of an ideal gas

[MexChemE]

Hello PF! Consider the free expansion of an ideal gas. The process occurs at constant temperature, therefore, ΔU = 0, Q = 0, and W = 0. Suppose we are given the initial and final pressures of the gas, and we calculate ΔG = nRT ln(P₂/P₁). As P₂ < P₁, ΔG < 0. This is intuitive, as a free expansion is clearly spontaneous. My question is, ΔG is commonly (physically) interpreted as the opposite of the "useful work" done by the system, but in this case the system does zero work. Does this mean ΔG is not an actual physical quantity, but a helpful theoretical measure of the useful work that can be extracted from the system?

Thanks in advance for any input!

 

[Bystander]

All it really tells you is the difference in free energy between the two states. It does not include any specification of path, or work done.

 

[Chestermiller]

My question is, ΔG is commonly (physically) interpreted as the opposite of the "useful work" done by the system, but in this case the system does zero work. Does this mean ΔG is not an actual physical quantity, but a helpful theoretical measure of the useful work that can be extracted from the system?

ΔG is commonly interpreted as the opposite of the maximum possible useful work (for a flow process) between the initial and final states.

Chet

 

[MexChemE]

Got it, so the system doesn't have to do work for it to have a negative change in free energy.

 

[LudusRex]

I would like to clarify that ΔG is indeed a physical quantity and is a measure of the change in the free energy of the system during the free expansion process. While it is true that the system does not do any work during free expansion, the change in free energy still reflects the spontaneous nature of the process. In fact, the negative ΔG value in this case indicates that the system is releasing energy during the expansion, which can be useful for other processes.

The interpretation of ΔG as the opposite of useful work is a simplification that is commonly used in thermodynamics. It is important to note that ΔG is a thermodynamic potential and is not directly related to the actual work done by the system. It is a measure of the maximum amount of work that can be obtained from the system under isothermal and isobaric conditions.

Furthermore, it is worth mentioning that the concept of free energy is useful in understanding and predicting the behavior of systems, especially in terms of their spontaneity and equilibrium. It is a theoretical construct that allows us to make predictions and calculations, but it is still based on physical principles and is a valid measure of the energy changes in a system.

In conclusion, ΔG is a physical quantity that represents the change in free energy during the free expansion of an ideal gas. Its negative value reflects the spontaneous nature of the process and its usefulness in predicting the behavior of systems. While it may not directly correspond to the actual work done by the system, it is still a valid and important concept in thermodynamics.