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.

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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.