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College Physics (Urone)
Found in: Page 548

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Short Answer

Which cyclical process represented by the two closed loops, ABCFA and ABDEA, on the PV diagram in the figure below produces the greatest net work? Is that process also the one with the smallest work input required to return it to point A? Explain your responses.

The greatest net work is produced by the process ABDEA. Yes, it has the least work input for reaching point A.

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Step by Step Solution

Definition of work in thermodynamics

Work done in a thermodynamic process is defined as the area under the P-V diagram in moving from initial volume \({{\rm{V}}_{\rm{1}}}\) to \({{\rm{V}}_{\rm{2}}}\).

\({\rm{W = }}\int\limits_{{{\rm{V}}_{\rm{1}}}}^{{{\rm{V}}_{\rm{2}}}} {{\rm{PdV}}} \)

For a closed cyclic process, the work done will then be the area enclosed by the graph of the closed cyclic process.

Comparing the two closed loops

From the diagram, it can be seen that the area of the closed-loop ABDEA is more than that of ABCFA. Hence, the net work produced in the process ABCDA is more than the other.

Work Input

As the input work is needed for two processes- CF for the cyclic process ABCFA and DE for the cyclic process ABDEA. The work needed in processes FA and EA is zero, as there is no change in volume in these processes.

The area under the curve represents the work needed for the process. If we compare the processes CF and DE the area under the curve is smaller for DE. Thus, the cyclic process ABDEA is the one with the least work input.

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