Explanation:
Given, $\mathrm{P}=2.5 \mathrm{~atm}, \mathrm{~V}_1=2.5 \mathrm{~L}, \mathrm{~V}_2=4.5 \mathrm{~L}$
$\Delta \mathrm{V}=4.50-2.5$
$\Delta \mathrm{V}=2 \mathrm{~L}$
For adiabatic process,
$q=0$
The first law of thermodynamics $\Delta \mathrm{U}=\mathrm{q}+\mathrm{W}$
When $\mathrm{q}=0$, then $\Delta \mathrm{U}=\mathrm{W}$
Now $\mathrm{W}=-\mathrm{P} \Delta \mathrm{V}$
$\Delta \mathrm{U}=-2.5 \times 2 \mathrm{~L}$ atm
$\Delta \mathrm{U}=-5 \mathrm{~L}$ atm
We know that $1 \mathrm{~L}$ atm $=101.3 \mathrm{~J}$
$\Delta \mathrm{U}=-5 \times 101.3 \mathrm{~J}=-506.5 \mathrm{~J} \approx-505 \mathrm{~J} \text {. }$