What is the formula for calculating nett work done in a thermodynamic cycle?

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SUMMARY

The nett work done in a thermodynamic cycle involving an ideal gas with two isobaric and two isothermal processes is calculated using the formula W = P1(V2 - V1)ln(P2/P1). The work done by the gas during the isothermal processes is expressed as nRTln(Vf/Vi), applicable specifically to the segments AB and CD. The isobaric processes are represented by segments BC and DA. Understanding the volume at points B and D is crucial for accurately determining the nett work done.

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  • Knowledge of thermodynamic processes (isobaric and isothermal)
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  • Basic calculus for logarithmic functions
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Wen
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An ideal gas is carried through a thermodynamic cycle consisting of 2 isobaric and 2 isothermal processes.

Show that the nett work done is

W=P1( V2-V1)ln ( P2/P1)

i am really stuck at this qn for very long. Please help me
 

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I assume that you mean you have been working on it for a long time! Show us what you think you do understand about the problem and what work you have already done.
 
i know that Work done by the gas is
nRTIn( Vf/Vi) and this is only for the two isothermal processes
Since BC and DA are isobaric, the 2 isothermal processes are AB and CD.
The nett work done is the shaded area in the diagram.
But i do not know the volume of the gas at B & D.
 

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