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.
(b) If an expansion occurs (V2 > V1) use Equation 1 to deduce
whether there will there be an increase or decrease in the
entropy of the gas.
(c) The ideal gas law states that pV = nRT, where p is the
pressure of the gas. Use this expression and Equation 1 to
obtain an equation relating the entropy change to the initial
and final pressures (p1 and p2). (Note that n,R and T will
be constant at the two different pressures).