# Thermodynamic potentials

1. ### failexam

492
1. The problem statement, all variables and given/known data

1. Explain the term thermodynamic potential.

2. Explain the motivations for defining the enthalpy, the Helmholtz free energy and the Gibbs free energy.

3. The Helmholtz and the Gibbs free energy are measures of the distance to thermodynamic equilibrium. Explain.

2. Relevant equations

H = U + PV
F = U - TS
G = U + PV - TS

3. The attempt at a solution

1. The word thermodynamic is used because the potentials make sense only in the theory of thermodynamics?

The word potential in mechanics refers to the integral of force with respect to distance, however I don't see how that definition extends over to the thermodynamics.

2. Enthalpy, Hemlholtz free energy and Gibbs free energy are simply different combinations of some basic functions, i.e. U, PV and TS.

U is a number that has been found to be invariant for a closed system and for some unknown reason is called energy. This so-called energy can transfer itself from one system to another, however no amount of itself is lost or created in the process.

The transfer of energy takes place only via contact of particles on the boundary of the systems.

Upon contact, particles in the absorbing system either

a) translate from one region of space to another, thereby increasing the volume occupied by the giving system. This type of transfer is called work.

b) do not translate from one region of space to another, thereby retaining the volume originally occupied by the giving system. This type of transfer is called heating/cooling.

a) PV refers to the work done in increasing the volume occupied by a system by V while it is at a pressure P?????

b) TS refers to ?????

????????

2. ### Mapes

2,532
Hint: For a closed, adiabatic system at constant volume ($dU=T\,dS-P\,dV=0$), energy U is minimized (that's what $dU=0$ implies). But not all systems have the same constraints. Some are at constant volume and constant temperature ($dV=dT=0$). Some are at constant pressure and adiabatic ($dP=dS=0$). Some are at constant pressure and constant temperature ($dP=dT=0$). How can we adapt energy to get useful parameters to minimize under these various conditions?

This statement is true, but here you're redefining V as a change in volume. This isn't the case in the original equations; V is the system volume. $\Delta V$ is used to denote a change in volume, and mechanical work at constant pressure is $P\,\Delta V$.