Statement I For an adiabatic process Q=0. If "work done" W is taken positive when done on the system, then the first law gives ∆U=Q+W=0+W=W Thus if work is done on the system ( W>0 ), its internal energy increases ( ∆U>0 ). Statement II In a free (Joule) expansion the external pressure P‌ext ‌=0, so W=∫PextdV=0 Hence no work is done during the free expansion of an ideal gas. Both statements are therefore true.