3. The entropy change, ΔS, associated with the isothermal (i.e. constant temperature) change in volume of n moles of an ideal gas from volume V1 to volume V2 is given by the equation ΔS = nR ln(V2/V1) where R is the gas constant. (a) If a compression occurs (V2 < V1) use Equation 1 to deduce whether there will there be an increase (ΔS is positive) or decrease (ΔS is negative) in the entropy of the gas.
If then and then that means negative and therefore the complete product is negative too. Thus is negative so there is a decrease in the entropy of the gas.