The entropy of the gas shoud NOT CHANGE during an ISOTHERMAL compression. It will in other forms of compression yes, but isothermal means the temp (and thus the sign of heat from enthropy) will NOT change. Remember, heat is a product of entropy, always in evidence when there is entrhopy. In isothermal compression, there is no heat change. Thus, no increase in heat means no change of enthropy during (and only during) isothermal compression. Other forms of compression will show increased enthropy expressed by heat increase. (remember, gasses produce an incresing amount of heat in relation to the entropy they are suffering. enthropy is inatedly the inability of something to go against its nature, thus forcing it into phy/chem reascions.)
(wow, its been awhile since I studied this in college. I'm afraid if I say too much, I'll complicate things. By the time I was in Phy. II in college....well, lets just say if a little knowledge is a dangerous thing, I was a potential threat to mankind)