For a reversible process involving only pressure-volume work

A. (dF)_{T, P} < 0

B. (dF)_{T, P} > 0

C. (dF)_{T, P} = 0

D. (dA)_{T, V} < 0

Answer: Option C

Solution(By Examveda Team)

Here the $$F$$ is Gibbs free energy and $$A$$ is Helmholtz free energy.
Since for an reversible process $$Tds = dU + PdV$$
For, constant temperature and constant pressure process the above equation can be written as
$$\eqalign{ & d\left( {TS - U} \right) = PdV \cr & \Rightarrow d\left( { - A} \right) > PdV \cr & \Rightarrow {\left( {dF} \right)_{T,\,P}} = 0. \cr} $$
For reversible process.