One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown In the graph below. If the work done along the solid line path is `W_(s)` and that along the the dotted line path is `w_(d)`, then the integer closest to the ratio `w_(d)//w_(s)` is

Answer

` to 2`

Explanation

Horizontal dotted lines indicate the work of constant pressure, each given by `PDeltaV`. Vertical dotted lines indicate that work done is zero because volume remains constant
`W_(d)=(4.0)xx1.5)+(1.0xx1.0)+(0.75xx2.5)L"atm"=6+1+1.815=8.875 L "atm"`
Solid line indicates isothermal reversible expansion. It is isothermal because `PV` is constant
`:. W_(s)=2.303nRT log V_(2)//V_(1)`
`=2.303PVlog V_(2)//V_(1) (PV=nRT)`
`=2.303xx2log"(5.5)/(0.5)(PV=2 L "atm")`
`=4.61 L"atm"`
Hence `=(W_(d))/(W_(s))=(8.875)/(4.61)=2`