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Question
What will be the work done on an ideal gas enclosed in a cylinder, when it is compressed by a constant external pressure, pext in a single step as shown in figure. Explain graphically.
Solution
Assumption: Cylinder is filled with one mole gas, and the piston is frictionless. Let the pressure of gas inside be p and the volume of gas be \[\ce{V_{I}}\].
Piston is moved towards the inside to make the external pressure \[\ce{(P_{ext})}\] equal to p. Now, let us assume that this change takes place in a single step, hence, \[\ce{V}\] is the final volume. The work done by the piston is depicted in the graph shown below by shading the area.
PextΔV = AV1 × (V1 – V2)
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