A certain gas undergoes constant temperature expansion from `264 mL` to `971 mL`. Calculate the work done in joules) by the gas if it expands (i) against a vaccum and (ii) against a constant pressure of 4 atm.
Strategy : Use to calculate the work done by the gas on the surrounding, i.e.,
`w = - P Delta V`
where `P` is the oppsoing external atmospheric pressure and `Delta V`, the change in volume, is given by `V_(f) - V_(i)`, Also, convert the initial and final volumes in liters.

Explanation

(i) Since the external pressure is zero, the work done is
`W = - P Delta V`
`= - 0 (0.971 L - 0.364 L)`
`= 0`
(ii) Here the external pressure is 4 atm. So
`w = - P Delta V`
` = - (4 atm) (0.971 L - 0.264 L)`
`= - 2.83 L atm`
Using the conversion factor
`1 L atm = 101.3 J`
we can write
`w = - 2.83 L atm xx (101.3J)/(1 L atm)`
`= - 286 J`