Question

An expression for Gibbs free energy is:

• A. \( H - TS \)
• B. \( U - TS \)
• C. \( dS_{\text{system}} + dS_{\text{surroundings}} \)
• D. \( dU = T dS - P dV \)

Hint:

Gibbs free energy: \( G = H - TS \). It predicts spontaneity at constant temperature and pressure — a negative \( \Delta G \) implies a spontaneous process.

Answer 1

The Correct Option is A

Step 1: Definition of Gibbs Free Energy
Gibbs free energy (\( G \)) is a thermodynamic potential that measures the maximum reversible work that a thermodynamic system can perform at constant temperature and pressure. It helps predict the spontaneity of a process. Step 2: Expression
The formula for Gibbs free energy is: \begin{equation} G = H - TS \end{equation} where:
\( G \) = Gibbs free energy
\( H \) = Enthalpy of the system
\( T \) = Absolute temperature in Kelvin
\( S \) = Entropy of the system Step 3: Evaluating Other Options
- (B) \( U - TS \): This is not the standard Gibbs free energy relation; it resembles Helmholtz free energy \( A = U - TS \).
- (C) \( dS_{\text{system}} + dS_{\text{surroundings}} \): Represents total entropy change, related to the second law, not Gibbs energy.
- (D) \( dU = TdS - PdV \): This is a thermodynamic identity for internal energy, not Gibbs free energy. Conclusion: The correct expression for Gibbs free energy is \( G = H - TS \).