# Thermodynamic potentials

by failexam
Tags: potentials, thermodynamic
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 $P\,\Delta V$.