Question

For an isolated system, $\Delta U=0$ , then

• A. $\Delta S=0$
• B. $\Delta S<0$
• C. $\Delta S>0$
• D. The value of $\Delta S$ cannot be predicted

Answer 1

Answer: (C)

For an isolated system, $\Delta U=0$ and for a spontaneous process, total entropy change must be positive.
For example, consider the diffusion of two gases $A$ and $B$ into each other in a closed container which is isolated from the surroundings.
The two gases $A$ and $B$ are separated by a movable partition. When partition is removed, the gases begin to diffuse into each other and the system becomes more disordered. It shows that $\Delta S>0$ and $\Delta U=0$ for this process.
Morever, $\Delta S=q_{rev}/T=\Delta H/T$
$=\Delta U+p\Delta V/T=p\Delta V/T$
i.e. $T\Delta S$ or $\Delta S>0$