State the first law using \(Q>0\) into the system and \(W>0\) done by the system.

A system receives \(300\,\mathrm{J}\) of heat and does no work. Find \(\Delta U\).

A gas absorbs \(500\,\mathrm{J}\) of heat and does \(120\,\mathrm{J}\) of work. Find \(\Delta U\).

A gas releases \(200\,\mathrm{J}\) of heat and has \(150\,\mathrm{J}\) of work done on it. Find \(\Delta U\).

A system has \(\Delta U=250\,\mathrm{J}\) while doing \(90\,\mathrm{J}\) of work. Find \(Q\).

An adiabatic expansion does \(400\,\mathrm{J}\) of work. Find \(\Delta U\).

A gas is compressed adiabatically by an external agent doing \(700\,\mathrm{J}\) of work on the gas. Find \(Q\), \(W\), and \(\Delta U\).

A gas completes a cycle and does \(1.2\,\mathrm{kJ}\) of net work. Find net heat transfer and explain the sign.

A gas is taken from \(A\) to \(B\) with \(Q=Q_0\). Then it is returned to \(A\) adiabatically while work \(W_{\mathrm{on}}\) is done on it. Derive \(W\) for the first path in terms of \(Q_0\) and \(W_{\mathrm{on}}\).

A system undergoes three processes that return it to the initial state. Given \((Q_1,W_1)\), \((Q_2,W_2)\), and \(W_3\), derive \(Q_3\), and state which assumption makes the result possible.