This question is asking us to determine a true statement regarding entropy. Let's look at each answer choice to see what is true about entropy and what isn't.

• The entropy of a system, whether it is isolated or non-isolated, can only increase.

This above statement is not true. While it's true that the entropy in an isolated system can only increase, the entropy in a non-isolated system can either increase or decrease. However, for the entropy to decrease in a non-isolated system, the entropy of the surroundings needs to increase by a greater amount.

• The entropy of a system can decrease, but only if the system is isolated and the process is irreversible.

This is another false statement. Once again, the entropy of an isolated system cannot decrease; it can only increase. Furthermore, only irreversible processes will result in an increase of entropy in such systems.

• The entropy of a system can decrease only in the case of a reversible adiabatic process.

Again, this is another false statement. The change in entropy of a system that is associated with a truly reversible process can be shown mathematically by the following equation:

\(\displaystyle \Delta S=\frac{Q}{T}\)

This equation shows that in a reversible process in which an infinitesimal amount of heat is added to (or taken away from) a system at a given temperature, the change in entropy of that system can be calculated. There are no truly reversible processes that occur in nature, as such a process would take an infinite amount of time.

In an adiabatic process, there is no heat transfer. Thus, the \(\displaystyle Q\) term in the above equation is equal to \(\displaystyle 0\). Consequently, there is no change in the entropy of the system.

• The entropy of a non-isolated system can decrease only if the entropy of its surroundings increases by a greater amount.

This is a true statement. In any non-isolated system, such as a refrigerator, the entropy can certainly decrease. However, since all irreversible processes must result in an increase in entropy in the universe as a whole (second law of thermodynamics), the entropy of the surroundings must decrease. We can express this mathematically as:

\(\displaystyle \Delta S_{system}+\Delta S_{surroundings}=\Delta S_{universe}>0\)

As can be seen by the above equation, if the \(\displaystyle \Delta S_{system}\) term is negative, then the \(\displaystyle \Delta S_{surroundings}\) term must not only be positive, but it must also be of greater magnitude.

For an isobaric process, the pressure is constant. Therefore, on a P-V diagram, the object will have the same pressure. Since pressure is on the y-axis, that means that we will have a straight horizontal line at the initial pressure.

For an isochoric process, the volume remains constant. Therefore, in a P-V diagram, for every pressure, we will have the same volume. Since volume is on the \(\displaystyle x\)-axis, this will result in a vertical line at the initial volume (\(\displaystyle x=V\)).