The thermodynamic criterion/criteria for a spontaneous process is/are
Show Hint
- \( \Delta U>0 \) at constant \( S \) and \( V \)
- \( \Delta S>0 \) at constant \( U \) and \( V \)
- \( \Delta(H - TS)>0 \) at constant \( T \) and \( P \)
- \( \Delta(U - TS)<0 \) at constant \( T \) and \( V \)
The Correct Option is B, D
Solution and Explanation
The correct thermodynamic criteria for spontaneity under different constraints are:
-
(A) \( \Delta U > 0 \) at constant \( S \) and \( V \):
This is incorrect. At constant entropy and volume, a spontaneous process is characterized by minimum internal energy, so \( \Delta U < 0 \) is required. WRONG -
(B) \( \Delta S > 0 \) at constant \( U \) and \( V \):
This is correct. At constant internal energy and volume, spontaneity is driven by an increase in entropy. CORRECT -
(C) \( \Delta(H - TS) > 0 \) at constant \( T \) and \( P \):
This corresponds to \( \Delta G > 0 \), which means non-spontaneity. For spontaneity, \( \Delta G < 0 \). WRONG -
(D) \( \Delta(U - TS) < 0 \) at constant \( T \) and \( V \):
This expression represents the Helmholtz free energy, \( A = U - TS \), and for spontaneity at constant \( T \) and \( V \), \( \Delta A < 0 \) is the correct criterion. CORRECT
\[ \boxed{\text{Correct options: (B) and (D)}} \]
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