One mole of a gas expands by $3 L$ against a constant pressure of $3$ atmosphere. Calculate the work done in Joules.

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Solution

The work done $(W)$ when the gas expands at constant pressure $P (= 3 a t m)$ from volume $V_{1}$ to $V_{2}$ is given by
$W = - \int_{V_{1}}^{V_{2}} P d v$
$= - P \int_{V_{1}}^{V_{2}} d v$
$= - P (V_{2} - V_{1}) = - P Δ V$
where, negative sign indicates work done by the system.
Here $△ V = 3 L$
We know, $1 L$ atmosphere $= 101.325 J$
Thus, $W = - 9 \times 101.325 J = - 911.925 J o u l e s$

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