The part of the total energy of a system that accounts for the useful work done in a system is known as

Analyze the question The question asks which thermodynamic quantity represents the portion of a system's total energy that is available to do useful work.

Explain the concept

• Enthalpy change (ΔH): the heat absorbed or released at constant pressure. It is the total heat content change, not just the useful work part.
• Entropy (S): a measure of disorder or randomness. It describes energy that is unavailable for work, not the useful part.
• Gibbs free energy (G): the energy available to do useful (non-expansion) work at constant temperature and pressure.

The relationship is:

ΔG = ΔH − TΔS

Here, ΔH is the total heat energy change, and TΔS is the energy tied up in disorder (unavailable for work). What remains, ΔG, is the "free" energy that can be used to do useful work.

Solution

1. Enthalpy is total heat content, so A is not the answer.
2. Entropy is a measure of disorder, so D is not the answer.
3. Gibbs free energy is the part of the energy that can do useful work, so C fits.
4. Since C is correct, B (None of the above) is wrong.

Answer: C. Gibb's free energy

Exam tip Remember "free = usable." Gibbs free energy is the energy that is free to do work. Also remember the sign rule: if ΔG is negative, the reaction is spontaneous.