Explanation:
Since \(U\) is a state function, \(\Delta U\) depends only on the initial & final states and not on the path taken by the gas to go from one state to other. However, \(\Delta Q\) and \(W\), in general depend on the path taken to go from the initial to final states.
Thus, from the first law of thermodynamics, i.e.
\(\Delta Q-W=\Delta U\)
\(\text { It is clear that } \Delta Q-W \text { is path }\)independent.
Also, when \(\Delta U=0 \Rightarrow \Delta Q=W\)
Hence, heat supplied to the system is used up entirely for doing work on the surrounding.
So option (3) is correct.