A thermally insulated vessel is partitioned into two parts so that the volume of one part is `n = 2.0` times greater than that of the other. The smaller part contains `v_1 = 0.30` mole of nitrogen, and the greater one `v_2 = 0.70` mole of oxygen. The temperature of the gases is the same. A hole is punctured in the partition and the gases are mixed. Find the corresponding increment of the system's entropy, assuming the gases to be ideal.

Explanation

Let `V_1 = V_0, n V_0`
Since the temperature is the same, the required entropy change can be calculated by considering isothermal expansion of the gas in either parts into the whole vessel.
Thus `Delta S = Delta S_I + Delta S_(II) = v_1R 1n (V_1 + V_2)/(V_1) + v_2 R 1n (V_1 + V_2)/(V_2)`
=`v_1 R 1n (1 + n) + v_2 R 1n (1 + n)/(n) = 5.1 J//K`.