A gas is allowed to expand in a well insulated container against a constant external pressure of $2.5\text{atm}$ from an initial volume of $2.50\text{L}$ to a final volume of $4.50\text{L}$. The change in internal energy $\Delta U$ of the gas in joules will be

Solution & Explanation

\textbf{Answer:} (C) $-505\text{J}$ \textbf{Solution:} A well-insulated container means the process is adiabatic, so $q=0$. By the first law $\Delta U=q+w=w$. The work done on the gas against a constant external pressure is $w=-p_{ext}\Delta V=-2.5\text{atm}\times (4.50-2.50)\text{L}=-5\text{Latm}$. Converting, $-5\times 101.3\text{J}\approx -506.5\text{J}\approx -505\text{J}$.