For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0\), and \(w=0\). (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. (c) In thermodynamics, what is the "driving force" for the expansion of the gas?

Gibbs Free Energy (G) is a fundamental concept in thermodynamics that helps determine whether a process will occur spontaneously. It’s an energy measure that combines the system's enthalpy (H), temperature (T), and entropy (S) to predict the favorability of a chemical reaction or physical change. A spontaneous process is characterized by a decrease in Gibbs Free Energy ()
In the case of isothermal expansion of a gas into a vacuum, where
Since the change in enthalpy (
A negative value for )

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it is widely accepted that processes tend to move towards a state of increased entropy. During the isothermal expansion of a gas, as the volume of gas increases, so does the entropy, because the gas molecules have more space to occupy and can therefore arrange themselves in a greater number of ways. This increase in entropy (
In our discussed exercise, the expansion into a vacuum presents no opposition to this spreading out of molecules, causing an unequivocal rise in entropy. This aligns with the second law of thermodynamics, which basically states that for any spontaneous process, the entropy of the universe increases. Therefore, )

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. It involves studying systems as they move towards thermal equilibrium, where no net transfer of energy occurs. The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transformed from one form to another. This is why, in our isothermal expansion example, even though the internal energy change (
Thermodynamics also covers the concepts of heat transfer, work done by or on the system, the thermodynamic properties of materials, and the laws that describe the transfer and transformation of energy. The phenomenon of gas expanding into a vacuum without doing work and without heat exchange is a unique scenario perfectly encapsulated by thermodynamic principles.

A spontaneous process is one that occurs without the need for external energy. It’s driven by a decrease in Gibbs Free Energy, an increase in entropy, or both. For a process to be spontaneous at all temperatures, its entropy must increase, as indicated by a positive change in entropy (
In the scenario of an isothermal expansion of a gas into a vacuum, we have a clear example of a spontaneous process. There's no energy input, yet the gas expands due to the natural predisposition towards a state of higher entropy. This expansion is spontaneous despite no work being performed and no heat exchange, again confirming to the basic premise that systems will spontaneously evolve towards configurations that maximize their entropy.

The concept of internal energy (
When examining isothermal processes, such as the isothermal expansion into a vacuum, the temperature of the system remains constant. Since temperature is a measure of the average kinetic energy of the molecules in a gas, and )