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(A) For an ideal gas in an isolated system,the process of mixing is spontaneous and occurs at constant temperature (isothermal process).Since the syst

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zero,positive

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(A) For an ideal gas in an isolated system,the process of mixing is spontaneous and occurs at constant temperature (isothermal process).Since the system is isolated,there is no exchange of heat with the surroundings $(q = 0)$ and no work is done $(w = 0)$,so $\Delta U = 0$.For an ideal gas,enthalpy change is given by $\Delta H = \Delta U + \Delta(PV) = \Delta U + \Delta(nRT)$. Since $T$ is constant and $\Delta U = 0$,$\Delta H = 0$.When the partition is removed,the gases mix,which increases the randomness of the system. Therefore,the entropy of the system increases,meaning $\Delta S > 0$ (positive).Thus,the change in enthalpy is zero and the change in entropy is positive.

An isolated box,equally partitioned,contains two ideal gases $A$ and $B$ as shown in the figure. When the partition is removed,the gases mix. The changes in enthalpy $(\Delta H)$ and entropy $(\Delta S)$ in the process,respectively,are

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