One mole of an ideal monatomic gas at absolute temperature \( T \) undergoes free expansion to double its original volume, so that the entropy change is \( \Delta S_1 \). An identical amount of the same gas at absolute temperature \( 2T \) undergoes isothermal expansion to double its original volume, so that the entropy change is \( \Delta S_2 \). The value of \( \frac{\Delta S_1}{\Delta S_2} \) (in integer) is: