Question

The maximum work obtained from a reversible process is given as:

• A. \( -\Delta A \)
• B. \( \Delta A \)
• C. \( -\Delta G \)
• D. \( \Delta G \)

Hint:

At constant \(T, V\): \( -\Delta A = \) maximum work
At constant \(T, P\): \( -\Delta G = \) maximum useful work

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Work in thermodynamics can be classified into total work and non-expansion (useful) work. Thermodynamic potentials like Helmholtz free energy (\(A\)) and Gibbs free energy (\(G\)) relate directly to these work terms during reversible processes.
Step 2: Key Formula or Approach:
1. Helmholtz Free Energy (\(A = U - TS\)).
2. Gibbs Free Energy (\(G = H - TS\)).
: Detailed Explanation:
1. For a reversible isothermal process, the decrease in Helmholtz free energy (\(-\Delta A\)) is equal to the maximum total work (\(W_{\text{rev, max}}\)) that can be done by the system.
\[ W_{\text{max}} = -\Delta A \]
2. The decrease in Gibbs free energy (\(-\Delta G\)) represents the maximum non-expansion work (useful work like electrical work) that can be obtained from the system.
Since the question asks for "maximum work" without specifying "useful", it refers to the total work associated with Helmholtz free energy.
Step 3: Final Answer:
The maximum work is given by \(-\Delta A\).