Question
Among the following which one term does not represent Gibbs free energy ?
This question was previously asked in
CUET PG 2026 Agri-Business Management Question Paper (25-Mar-2026) (Shift 2)
The correct answer is
$G=U+TS$
Gibbs Free Energy Formulas Explained
Gibbs free energy ($G$) represents the maximum amount of non-expansion work that can be extracted from a closed system at constant temperature and pressure. It is a thermodynamic potential.
We need to identify which given expression does not correctly represent Gibbs free energy ($G$).
Thermodynamic Relationships
Key thermodynamic relationships are:
- Internal Energy: $U$
- Enthalpy: $H = U + PV$
- Helmholtz Free Energy: $F = U - TS$
- Gibbs Free Energy: $G = H - TS$
Analyzing the Options
Let's examine each option based on the definition $G = H - TS$ and the relationship $H = U + PV$.
-
Option 1: $G = U + TS$
This expression is not a standard formula for Gibbs free energy. It resembles the Helmholtz free energy formula ($F = U - TS$) but with a positive sign for the $TS$ term. -
Option 2: $G = F + PV$
Substitute $F = U - TS$: $G = (U - TS) + PV$ $G = U - TS + PV$ This matches a known form of Gibbs free energy. -
Option 3: $G = H - TS$
This is the fundamental definition of Gibbs free energy. -
Option 4: $G = U - TS + PV$
Substitute $H = U + PV$ into the definition $G = H - TS$: $G = (U + PV) - TS$ $G = U - TS + PV$ This is a valid expression for Gibbs free energy.
Conclusion on Gibbs Free Energy Representation
Options 2, 3, and 4 represent valid forms of Gibbs free energy ($G$). Option 1, $G = U + TS$, does not represent Gibbs free energy.
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