Question

Among the following, the correct condition(s) for spontaneity is(are)

• A. \(\left( \Delta G_{\text{sys}} \right)_{P,T}<0\)
• B. \(\left( \Delta A_{\text{sys}} \right)_{V,T}<0\)
• C. \(\left( \Delta H_{\text{sys}} \right)_{P,S}<0\)
• D. \(\left( \Delta U_{\text{sys}} \right)_{V,P}<0\)

Hint:

For a process to be spontaneous, \(\Delta G_{\text{sys}}<0\) is the key criterion at constant pressure and temperature.

Answer 1

The Correct Option is A

Step 1: Analyze each option.
- Option (A): This is correct. For spontaneity, Gibbs free energy (\(\Delta G\)) must be negative at constant pressure (P) and temperature (T), as per the criterion for spontaneous processes in thermodynamics.
- Option (B): This is incorrect. The spontaneity condition is not defined for Helmholtz free energy (\(\Delta A\)) under constant volume (V) and temperature (T).
- Option (C): This is incorrect. The spontaneity of a process is not determined by enthalpy change (\(\Delta H\)) at constant pressure and entropy (S).
- Option (D): This is incorrect. The spontaneity condition is not defined for internal energy change (\(\Delta U\)) at constant volume and pressure.

Final Answer: \[ \boxed{\text{The correct answer is (A).}} \]