How Does Entropy Change During Gas Compression and Expansion?

[zezima1]

Suppose we have a closed cylinder with a partition. In one chamber is a gas, in the other is nothing. Now suppose we quickly remove the partition. The gas expands freely without work being done. Thus the entropy increases, because the gas doesn't "lose" energy.
So that explains how a gas increases its entropy during an expansion. But what about a compression. Suppose you slam the piston down on a gas faster than it can react. Then the proces is not quasistatic. So what is the work done on the gas in this case? If the entropy should increase it must be bigger than the work done in a quasistatic compression. But how does this happen?

 

[eljose79]

I would like to clarify and add some additional information to this forum post. Firstly, it is important to note that the concept of entropy is related to the amount of disorder or randomness in a system. In the context of gases, it is a measure of the number of microstates (possible arrangements of molecules) that the gas can occupy at a given temperature and pressure.

In the scenario described, where a gas expands freely without work being done, the entropy of the gas increases because it now has more microstates available to it. This is due to the fact that the gas molecules are now able to spread out and occupy a larger volume, rather than being confined to a smaller chamber. This increase in entropy is a natural and spontaneous process, as the gas molecules will always tend to move from a region of higher concentration to a region of lower concentration.

On the other hand, in the case of compression, the gas molecules are being forced into a smaller volume, resulting in a decrease in entropy. This process requires work to be done on the gas, as the molecules are being pushed closer together against their natural tendency to spread out. In a quasistatic compression, the work done on the gas is equal to the decrease in entropy. However, in a non-quasistatic compression (such as the scenario described in the forum post), the work done may be greater than the decrease in entropy. This is because the compression is happening too quickly for the gas molecules to adjust and reach equilibrium, leading to a higher energy state and therefore a higher entropy.

In summary, the increase in entropy during expansion and the decrease in entropy during compression are both a result of the natural tendency of gas molecules to spread out and occupy more space. In the case of a non-quasistatic compression, the work done on the gas may be greater than the decrease in entropy, but this does not violate the fundamental principle of entropy. It is simply a result of the compression happening too quickly for the gas molecules to adjust and reach equilibrium.