Question

Which of the following relation is not correct?

• A. \( \Delta H = \Delta U - P \Delta V \)
• B. \( \Delta U = q + W \)
• C. \( \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \geq 0 \)
• D. \( \Delta G = \Delta H - T \Delta S \)

Hint:

In thermodynamics, always verify the sign conventions in equations. For example, the correct relation between enthalpy (\( \Delta H \)) and internal energy (\( \Delta U \)) is \( \Delta H = \Delta U + P \Delta V \).

Answer 1

The Correct Option is A

Step 1: Analyze each relation. 1. Relation (A): \( \Delta H = \Delta U -P \Delta V \) 
This is incorrect. The correct relation is \( \Delta H = \Delta U + P \Delta V \) (for constant pressure). 2. Relation (B): \( \Delta U = q + W \) 
This is correct. It represents the first law of thermodynamics, where \( \Delta U \) is the change in internal energy, \( q \) is heat, and \( W \) is work. 3. Relation (C): \( \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \geq 0 \) 
This is correct. It represents the second law of thermodynamics, stating that the total entropy of a system and its surroundings always increases or remains constant for a spontaneous process. 4. Relation (D): \( \Delta G = \Delta H -T \Delta S \) 
This is correct. It represents the Gibbs free energy equation, where \( \Delta G \) is the change in Gibbs free energy, \( \Delta H \) is the change in enthalpy, \( T \) is temperature, and \( \Delta S \) is the change in entropy. 
Step 2: Determine the incorrect relation. 
The incorrect relation is (A) \( \Delta H = \Delta U - P \Delta V \).