Answer
$400\text{ J}$
Work Step by Step
Initial volume of $CH_4=2L$
When combusted in excess oxygen
$CH_4+2O_2$ gives $CO_2+2H_2O$
Initially we have 2L of methane and excess of oxygen
After reaction we have 2L of $CO_2$ and excess oxygen -reacted oxygen
So 4L of oxygen will react with 2L of methane.
Difference in the volume of product and reactant is 4L
work done $=pdv$
work done $=1\text{ bar}\times(1\text{ atm}/1.01325\text{ bar})\times4L$
$Workdone=3.95\text{ atm\cdot L}$
As $1\text{ atm}\cdot L=
101.325\text{ J}$, we have:
$3.95\cdot 101.325\approx 400\text{ J}$
