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

Answer

2

Explanation

Process shown by solid line is reversible isothermal So, work
`W_(s)= -4xx0.5 ln(5.5//0.5)`
`= -2 ln 11 L"atm"`
For dotted process (three step irreversible) work done wil be
`W_(d)= -{4xx1.5+1xx1+(2)/(3)xx2.5} L atm. = -{6+1+(5)/(3)}L atm. = -(26)/(3)L atm`.
so, `(W_(d))/(W_(s))=(26)/(3xx2ln11)~~2`