A piston is cleverly designed so that it extracts the maximum amount of work out of a chemical reaction, by matching `P_("estera")` to the `P_("istema")` at all times. This 8cm diameter piston initially holds back 1 mol of gas occupying 1 L, and comes to rest after being pushed out a further 2 L at `25^(@)C.` After exactly half of the work has been done, the piston has travelled out a total of .

Options

A. `10.0 cm`
B. `11.2 cm`
C. `16.5 cm`
D. `20.0 cm`

Explanation

Total work done `(-w) = n RT ln "" (V _(2))/( 1) implies V _(2) = 1. 732 L`
Also `V = pir ^(2) h implies` When `V = 1 L : h _(1) = ( 1000 cm ^(3))/( 3. 14 xx 16 cm ^(2)) = 19. 9 cm implies (V _(2))/( V _(1)) = ( 17 32 )/( 1000) = ( h _(2))/( h _(1))`
`h _(2) - 19. 9 xx ( 1732)/(1000) = 34.5 cm implies` Distance travelled `= h _(2) - h _(1) = 14. 6 cm`