4 . 0L of an ideal gas is allowed to expand isothermally into...

In case of expansion, work is done by system.

Now, as we know that,

$W = - {P}_{ext .} ∆ V$

As the gas is expanding into vacuums which has no pressure, i.e.,

${P}_{ext .} = 0$

$∴ W = 0$

Hence, no work is done.

From first law of thermodynamics,

$\Delta U = q + W$

As the system is working at constant temperature, i.e., isothermally.

$∴ \Delta U = 0$

Hence $q = - W = 0$