Please send a solutions Pressure vs volume graphs for a cert

Pressure vs. volume graphs for a certain gas undergoing five different cyclic processes are shown below. During which cycle does the gas do the greatest positive work?

Solution

Work done by the gas is directly proportional to the area covered by the curve of the loop:

We see that area covered by cycle IV is greatest . <----- NOTE : cycle II has same magnitude as cycle IIII but has -ve sign (due to counterclock wise rotation)

then it is followed by cycle V . then cycle III .

After these three cycle I comes and then cycle II<----- it has less magnitude than cycle II by is -ve in sign

So,

ANSWER is : IV > V > III > II > I

So, cycle IV does the greatest work