For an irreversible 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 A

Solution(By Examveda Team)

Since for an spontaneous 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 spontaneous process.
Here the F is Gibbs free energy and A is Helmholtz free energy.