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: Evaluate each relationship. 1. Relationship (A): \( \Delta H = \Delta U -P \Delta V \)
This relationship is erroneous. The accurate relationship is \( \Delta H = \Delta U + P \Delta V \) (applicable under constant pressure conditions). 2. Relationship (B): \( \Delta U = q + W \) 
This relationship is accurate. It articulates the first law of thermodynamics, with \( \Delta U \) signifying the change in internal energy, \( q \) representing heat, and \( W \) denoting work. 3. Relationship (C): \( \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \geq 0 \) 
This relationship is accurate. It conveys the second law of thermodynamics, positing that the aggregate entropy of a system and its surrounding environment consistently increases or remains static during a spontaneous process. 4. Relationship (D): \( \Delta G = \Delta H -T \Delta S \) 
This relationship is accurate. It defines the Gibbs free energy equation, where \( \Delta G \) denotes the change in Gibbs free energy, \( \Delta H \) represents the change in enthalpy, \( T \) signifies temperature, and \( \Delta S \) indicates the change in entropy. 
Step 2: Identify the erroneous relationship. 
The incorrect relationship identified is (A) \( \Delta H = \Delta U - P \Delta V \).