Three moles of an ideal monoatomic gas undergoes a cyclic process as shown in the figure. The temperature of the gas in different states marked as 1,2,3 and 4 are 400K, by the gas during the process 1-2-3-4-1 is (universal gas constant is R)

Explanation

Process `1rarr2` and `3rarr4` are polytrophic and
process `2rarr3` and `4rarr1` are isobaric.
From the graph
`PproprArr(P)/(V)=KrArrPV^(-1)=KrArrx=-1`
Work done `W=W_(1rarr2)+W_(2rarr3)+W_(3rarr4)+W_(4rarr1)`
`=(nR)/(x-1)(T_(1)-T_(2))+P_(2)(V_(3)-V_(2))+(nR)/(x-1)[T_(3)-T_(4)]+P_(1)[V_(1)-V_(4)]`
`(nR)/(x-1)[T_(1)-T_(2)]+nR(T_(3)-T_(2))+(nR)/(x-1)[T_(3)-T_(4)]+nR[T_(1)-T_(4)]`
`=(nR)/(x-1)[T_(1)-T_(2)+T_(3)-T_(4)]+nR(T_(3)-T_(3)+T_(1)-T_(4))``=(nR)/(x-1)[T_(1)-T_(2)+T_(3)-T_(4)]+nR(T_(3)-T_(3)+T_(1)-T_(4))`
`=(3R)/(-1-1)[400-700+2500-100]`
`+3R(2500-700+400-1100)`
`=(3R)/(-1-1)[1100]+3R(1100)`
`=3R(1100)(1-(1)/(2))=1650R`