Entropy change: V, P, T

[rkang00]

How does entropy change with volume, pressure, and temperature changes? Basically: what happens to entropy if one of the three factors increases/decreases?

[Katie Sy 1L]

Higher volume leads to greater entropy because the larger the volume the more ways there are to distribute the molecules in that volume; the more ways there are to distribute the molecules (energy), the higher the entropy

The entropy of a system decreases with an increase in pressure. This is due to the inverse relationship between pressure and volume.

If you increase temperature, you increase entropy. More energy put into a system excites the molecules and the amount of random activity. As a gas expands in a system, entropy increases.

[Sydney To 1D]

The higher the temperature, the more thermal energy the system has and thus, the system has more ways to distribute that energy. The more ways there are to distribute energy, the higher the entropy. The larger the volume, the more ways to distribute the molecules in that volume. The more ways there are to distribute the molecules/energy, the higher the entropy. It is the opposite for pressure, however, due to the concept that pressure and volume are inversely proportional.

[2c_britneyly]

ΔS=q/T, so the higher the temperature, the smaller the change in entropy for the same amount of heat released or absorbed.
ΔS=nRlnV₂/V₁, so if there is a decrease in volume the ln term will become negative, and there will be a decrease in entropy. If volume increases, the ln term becomes positive, and there will be an increase in entropy.
Also, because we know pressure and volume are inversely related, we can modify the above equation to ΔS=nRlnP₁/P₂. If pressure increases, then entropy decreases, and vice versa.

[CHEM 14B Lover]

Why does higher pressure mean less entropy? Couldn't there still be an equal volume of gas but at higher pressure?