`1.0` mole of a monoatomic ideal gas is expanded from state (1) to state (2) as shown in the figure. Calculate ti work done for the expansion of gas from state (1) to state (2) at 298 K

Options

A. `-1717.46 J`
B. `+1717.46J`
C. `-1908.2J`
D. `+1908.2J`

Explanation

It is clear from the figure that the process has been carried out in infinite steps, hence it is isothermal reversible expansion.
`W =- 2 . 303 nRT log ""( V _(2))/( V _(1)) But, p _(1) V _(1) = p _(2) V _(2) implies (V_(2))/(V _(1)) = ( p _(1))/( p _()) = (2)/(2) = 2, W = - 2. 303 n RT log "" ( p _(1))/( p _(2))`
`=- 2. 303 xx 1 mol xx 8. 314 mol ^(-1) K^(-1) xx 298 K xx log 2 =- 2. 303 xx 8. 314 xx 298 xx 0. 2010 J =0 1717 . 46 J `