Expansion of a gas in vacuum is called free expansion. Calculate the work done and the change in internal energy when $1 \ L$ of ideal gas expands isothermally into vacuum until its total volume is $5 \ L$?

(A) Work done of a gas in vacuum is given by the formula $W = -p_{ext} \Delta V$.
Since the expansion occurs in vacuum,the external pressure $p_{ext} = 0$.
Therefore,$W = -0 \times (5 \ L - 1 \ L) = 0 \ J$.
For an ideal gas,the internal energy $U$ is a function of temperature only $(U = f(T))$.
Since the process is isothermal,the temperature remains constant $(\Delta T = 0)$,which implies that the change in internal energy $\Delta U = 0$.