Question

Which of the following relation is not correct?

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

Hint:

Enthalpy change, \( \Delta H \), is related to internal energy change by the equation \( \Delta H = \Delta U + P\Delta V \), which is crucial for understanding thermodynamic systems at constant pressure.

Answer 1

The Correct Option is A

Step 1: {Analysis of Relation A}
Relation (A) is identified as incorrect. The accurate formula for enthalpy change is \( \Delta H = \Delta U + P\Delta V \). Option (A) is erroneous as it incorrectly subtracts \( P\Delta V \) rather than adding it.
Step 2: {Validation of Relations B, C, and D}
Relation (B) is validated; the change in internal energy \( \Delta U \) equals the sum of heat absorbed by the system \( q \) and the work performed on the system \( W \), represented as \( \Delta U = q + W \).
Relation (C) aligns with the second law of thermodynamics, stipulating that the overall entropy change (system and surroundings) in a spontaneous process is non-negative (greater than or equal to zero).
Relation (D) represents the correct formulation of the Gibbs free energy equation.
Consequently, the correct option is (A).