Is internal energy a state function or a path function?

For a complete thermodynamic cycle, what is \(\Delta U\)?

Can two paths between the same states have different work values?

A process from \(A\) to \(B\) has \(\Delta U=120\,\mathrm{J}\) and \(W=50\,\mathrm{J}\). Find \(Q\).

Two paths connect the same states. Path 1 has \(W=200\,\mathrm{J}\); path 2 has \(W=80\,\mathrm{J}\). If \(\Delta U=60\,\mathrm{J}\), find \(Q\) for each path.

A cyclic process absorbs \(900\,\mathrm{J}\) of heat. Find the net work done by the system over the cycle.

A gas goes from \(A\) to \(B\) by a path with \(Q=500\,\mathrm{J}\) and \(W=180\,\mathrm{J}\). It returns from \(B\) to \(A\) with \(W=-80\,\mathrm{J}\). Find \(Q\) for the return path.

On a \(p\)-\(V\) diagram, why can work differ for two paths with identical endpoints?

A system moves from \(A\) to \(B\) along path 1 with heat \(Q_1\) and work \(W_1\). Along path 2, the work is \(W_2\). Derive \(Q_2\) in terms of \(Q_1,W_1,W_2\).

A closed cycle consists of expansion at pressure \(p_h\), cooling at constant volume, compression at pressure \(p_l\), and heating at constant volume. Derive the net heat absorbed over the cycle in terms of \(p_h,p_l,V_1,V_2\).