Figure 20.38 shows two quasistatic processes that take a sample of an ideal gas containing \(N\) particles from an initial state \(\left(P_{i}, V_{i}\right)\) to a final state \(\left(P_{f}, V_{f}\right)\). Process A is a one-step isentropic compression. Process \(B\) has two steps: an isochoric pressure increase to an intermediate state 1 followed by an isobaric decrease in volume. Express the changes in entropy for process \(A\) and process \(B\) in terms of the given quantities.

Data from Figure 20.38

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P P process B process A V