Calculate the work done by a gas as it is taken from 1 to 2,2 to 3 and 3 to 1 as shown. Also calculate the work done in cyclic process `1rarr2rarr3rarr1`

Explanation

The work done in a process is the area below the process in `P-V` diagram.
process `1rarr2`
`DeltaW_(1rarr2)=P_0(2V_0-V_0)=P_0V_0`
In the process `2rarr3`, volume remains same
`DeltaW_(2rarr3)=0`
process `3rarr1`:

`DeltaW_(3rarr1)=`area below the process `3rarr1`
`=-(1)/(2)(P_0+3P_0)(2V_0-V_0)`
`=-2P_0V_0`

Work done is negative because volume is decreasing work done in cyclic process:
`DeltaW_(cyclic)=DeltaW_(1rarr2rarr3rarr1)`
`=DeltaW_(1rarr2)+DeltaW_(2rarr3)+DeltaW_(3rarr1)`
`=P_0V_0+0-2P_0V_0`
`=-P_0V_0`