The differential form of the Helmholtz free energy—for a closed, one-component system—is given below. dA = -PdV - SdT Starting from A = U - TS, derive the above expression. Show that ΔA = ΔU - T ΔS. Be sure to clearly state any assumptions or conditions. The Helmholtz energy can be used to determine the spontaneity of a process in the same way as the Gibbs energy: dA = -PdV - SdT + ∑µi dNi at equilibrium dA = 0 Under what conditions and/or for what types of systems would it be easier to use the Helmholtz free energy, as opposed to the Gibbs free energy? Briefly explain.

The differential form of the Helmholtz free energy—for a closed, one-component system—is given below. dA = -PdV - SdT Starting from A = U - TS, derive the above expression. Show that ΔA = ΔU - T ΔS. Be sure to clearly state any assumptions or conditions. The Helmholtz energy can be used to determine the spontaneity of a process in the same way as the Gibbs energy: dA = -PdV - SdT + ∑µi dNi at equilibrium dA = 0 Under what conditions and/or for what types of systems would it be easier to use the Helmholtz free energy, as opposed to the Gibbs free energy? Briefly explain.