What is the pressure-volume work done by a gas during a constant-volume process?

A gas expands at constant pressure \(1.5\times10^5\,\mathrm{Pa}\) by \(0.020\,\mathrm{m^3}\). Find \(W\).

A gas is compressed at constant pressure \(2.0\times10^5\,\mathrm{Pa}\) from \(0.050\) to \(0.030\,\mathrm{m^3}\). Find \(W\).

A gas pressure varies linearly from \(1.0\times10^5\) to \(3.0\times10^5\,\mathrm{Pa}\) while volume increases from \(0.020\) to \(0.050\,\mathrm{m^3}\). Find the work done by the gas.

A gas expands with pressure \(p(V)=aV\), where \(a=4.0\times10^6\,\mathrm{Pa\,m^{-3}}\), from \(V=0.010\) to \(0.030\,\mathrm{m^3}\). Find \(W\).

A piston of area \(0.0040\,\mathrm{m^2}\) moves outward \(0.12\,\mathrm{m}\) against constant pressure \(1.8\times10^5\,\mathrm{Pa}\). Find the work done by the gas.

A gas follows \(p(V)=p_0(V_0/V)\) from \(V_0\) to \(3V_0\). Derive the work done by the gas.

Two processes connect the same volumes \(V_i\) and \(V_f\). One expands at high pressure \(p_h\), the other at low pressure \(p_l\). Which does more work and why?

A gas expands from \(V_1\) to \(V_2\) along \(p=a+bV\), with \(a,b>0\). Derive \(W\), then state the condition for positive work.

A rectangular cycle on a \(p\)-\(V\) diagram has corners \((V_1,p_1)\), \((V_2,p_1)\), \((V_2,p_2)\), and \((V_1,p_2)\), with \(V_2>V_1\) and \(p_2>p_1\). Derive the net work for clockwise and counterclockwise traversal.