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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.)

  1.  $\Delta U,\:\Delta S,\:Q$ are same
  2. $W,\:\Delta U,\:\Delta G,$ are same
  3. $\Delta S,\:W,\:Q$ are same
  4. $\Delta G,\:\Delta U,\:\Delta S$ are same
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