1.

Find the work done by an ideal gas during a closed cycle `1rarr2rarr3rarr4rarr1` as shown in figure.

Answer» Divide the cylics process `1rarr2rarr3rarr4rarr1` in two processes, `1rarrOrarr2` and `3rarrOrarr4`.
In two similar Deltas `12O` and `3O4`
`(3P_0-P_0)/(5V_0-V_0)=(4P_0-3P_0)/(V_4-V_3)impliesV_4-V_3=2V_0`
`DeltaW_(1rarrOrarr2)=(1)/(2)xx(3P_0-P_0)(5V_0-V_0)=4P_0V_0`
`DeltaW_(3rarrOrarr4)=-(1)/(4)xx(4P_0-3P_0)(V_4-V_3)`
`=-(P_0)/(2)xx2V_0=-P_0V_0`
`DeltaW_(1rarr2rarr3rarr4rarr1)=4P_0V_0-P_0V_0`
`=3P_0V_0`


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