Question

For an ideal gas undergoing reversible isothermal expansion, the function \( G \) and \( A \) are given as \( G = H - TS \) and \( A = U - TS \), respectively. Choose the correct answer from the options given below: (A) \( \Delta G = \Delta A \)
(B) \( \Delta(PV) = 0 \)
(C) \( \Delta G > \Delta A \)
(D) \( \Delta(nRT) = 0 \)

• A. (A) and (B) only
• B. (B), (C) and (D) only
• C. (C) and (D) only
• D. (A), (B) and (D) only

Hint:

For isothermal processes, the changes in Gibbs and Helmholtz free energies are equal, and \( \Delta(PV) = 0 \) for ideal gases.

Answer 1

The Correct Option is A

For an ideal gas undergoing a reversible isothermal expansion: - \( \Delta G \) is the change in Gibbs free energy, and \( \Delta A \) is the change in Helmholtz free energy. - Since the process is isothermal, the temperature \( T \) is constant, and hence, the change in entropy, \( \Delta S \), is zero. This means that \( \Delta G = \Delta A \). - For an ideal gas undergoing an isothermal process, \( \Delta(PV) = 0 \) as pressure and volume follow the ideal gas law. Hence, statements (A) and (B) are correct. Final Answer: \[ \boxed{\text{(1) (A) and (B) only}} \]