Question

What will be the work done on an ideal gas enclosed in a cylinder, when it is compressed by a constant external pressure, $p_{ext}$ in a single step as shown in Figure Explain graphically.

Answer 1

• If the work is done in a single step, it implies that it is an irreversible process.
• Work done during compression of a gas at a constant external pressure is given by the relation $W=-P_{Ext}\Delta V$ i.e. the product of the constant external pressure and the change in volume.
• Now, if we plot Pressure, $P$ on $y-$axis vs. Volume $V$ on $x-$axis graph for the given process, then we get the following figure:

• From this graph, one can obtain to be the work done on the ideal gas enclosed in the cylinder which is equal to the area covered by $P–V$ graph (shaded region)
• i.e. Work done = shaded Area = Area of shape $AB{V}_i{V}_f=-P_{Ext}\times \Delta V$