A gas is allowed to expand against a constant external pressure of 2.5 bar from an initial volume ' $x$ '…
A gas is allowed to expand against a constant external pressure of 2.5 bar from an initial volume ' $x$ ' $L$ to final volume of $4.5 \mathrm{~L}$. If amount of work done is $5 \mathrm{dm}^3$ bar, what is the value of ' $x$ '?
2.5 L
4.5 L
6.0 L
1.2 L
Solution
1.2 Work done $=-5$ bar. $\mathrm{dm}^3$ (due to expansion work done will be negative)
$\mathrm{W}=-\operatorname{Pext}\left[\mathrm{V}_2-\mathrm{V}_1\right] \quad\left(1 \mathrm{~L}=1 \mathrm{dm}^3\right)$
$-5 \text { bar- } \mathrm{dm}^3=-2.5 \text { bar }[4.5-\mathrm{x}] \mathrm{dm}^3$
$4.5-\mathrm{x}=\frac{5}{2.5}$
$\begin{aligned}
& 4.5-x=2 \\
& x=4.5-2 \\
& x=2.5 L
\end{aligned}$