Three identical closed systems of a pure gas are taken from an initial temperature and pressure $(T_{1},P_{1})$ to a final state $(T_{2},P_{2})$, each by a different path. Which of the following is $ALWAYS \: TRUE$ for the three systems ? ($\Delta$ represents the change between the initial and final states; $U,\:S,\:G,\:Q,\: and \:W$ are internal energy, entropy , Gibbs free energy, heat added and work done , respectively.)
- $\Delta U,\:\Delta S,\:Q$ are same
- $W,\:\Delta U,\:\Delta G,$ are same
- $\Delta S,\:W,\:Q$ are same
- $\Delta G,\:\Delta U,\:\Delta S$ are same