# Free energy in the free expansion of an ideal gas

• MexChemE
In summary, the conversation discussed the free expansion of an ideal gas at constant temperature, where ΔU, Q, and W are all equal to zero. The change in free energy, ΔG, was calculated and found to be negative, indicating that the free expansion is a spontaneous process. The question was raised about the interpretation of ΔG as the opposite of useful work, given that the system does not actually do any work in this case. It was concluded that ΔG is a theoretical measure of the maximum possible useful work that can be extracted from the system, regardless of whether work is actually done.

#### 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!

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.

MexChemE
MexChemE said:
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.

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.

## 1. What is free energy in the context of an ideal gas?

Free energy, also known as Gibbs free energy, is a thermodynamic quantity that measures the amount of energy available to do useful work in a system at constant temperature and pressure. In the case of an ideal gas, free energy is the energy that is available to do work as the gas expands and fills a larger volume.

## 2. How does free energy change during the free expansion of an ideal gas?

In the free expansion of an ideal gas, the volume of the gas increases and no external work is done. This means that the change in free energy, or ΔG, is equal to zero. This is because no energy is transferred between the system (the gas) and its surroundings during free expansion.

## 3. Is free energy conserved during the free expansion of an ideal gas?

Yes, free energy is a conserved quantity in the free expansion of an ideal gas. This is because, as mentioned before, no energy is transferred between the system and its surroundings during the expansion process.

## 4. Can the free expansion of an ideal gas be reversible?

No, the free expansion of an ideal gas is an irreversible process. This is because the gas expands into a larger volume without any external work being done, which cannot be reversed without adding energy to the system.

## 5. How is free energy related to entropy in the free expansion of an ideal gas?

In the free expansion of an ideal gas, there is an increase in entropy due to the gas molecules spreading out and becoming more disordered. This increase in entropy is reflected in the decrease in free energy, as ΔG is equal to the change in entropy, ΔS, multiplied by the temperature, T.