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

One mole of an ideal gas is taken from a to b along two paths denoted

1.	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» Solution :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`