Question

Describe the relationship between the free energy change for a spontaneous process and the amount of work that can be obtained from the process. Is this amount of work obtainable in “real” processes? Explain your reasoning.

Answer 1

• When a system changes from a well-defined initial state to a well-defined final state, the Gibbs free energy, ΔG, equals the work done/exchanged by the system with its surroundings, minus the work of the pressure forces.
• work: In thermodynamics, work performed by a closed system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system.

Gibbs energy is the maximum useful work that a system can do on its surroundings when the process occurring within the system is reversible at constant temperature and pressure. As in mechanics, where potential energy is defined as capacity to do work, different potentials have different meanings. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system. The work is done at the expense of the system’s internal energy. Energy that is not extracted as work is exchanged with the surroundings as heat.

The ΔG for a reversible process is equal to the maximum non-PV work that can be performed at constant temperature and pressure on a conservative system.

Consider the differential relationship between the Gibbs' free energy, enthalpy, and entropy:

dG=dH−d(TS)

From the definition of enthalpy, H=U+PV, where U is the internal energy. As a result,

dG=dU+d(PV)−d(TS)

From the first law of thermodynamics, dU=δq+δw, where δ indicates a path function.

dG=δq+δw+PdV+VdP−TdS−SdT

Work can be defined as

δw=δwPV+δwnon-PV,

where PV work defined from the perspective of the system is δwPV=−PdV. Non-PV work can be, e.g. electrical work (think electrochemistry).

From this, assuming that the process performed is reversible (in thermal equilibrium the whole way through), qrev=TdS, so:

dG=−SdT+VdP+δwnon-PV

In the end, we find that at constant temperature and pressure, the Gibbs' free energy corresponds to the maximum non-compression and non-expansion work that can be performed:

dG=δwnon-PV, const T & P