### All AP Physics 2 Resources

## Example Questions

### Example Question #1 : Other Thermodynamics Concepts

Which of the following is a true statement concerning the entropy of a system?

**Possible Answers:**

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

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

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

None of these.

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

**Correct answer:**

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

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:

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 term in the above equation is equal to . 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:

As can be seen by the above equation, if the term is negative, then the term must not only be positive, but it must also be of greater magnitude.

### Example Question #1 : Other Thermodynamics Concepts

Describe the pressure versus volume graph for an isobaric process, where stands for pressure.

**Possible Answers:**

Cubic -

Horizontal line -

Quadratic -

Linear -

Vertical line -

**Correct answer:**

Horizontal line -

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.

### Example Question #2 : Other Thermodynamics Concepts

Describe the graph of an isochoric process, where is the initial volume.

**Possible Answers:**

Cubic -

Quadratic -

Linear, going through origin -

Vertical line -

Horizontal line -

**Correct answer:**

Horizontal line -

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 -axis, this will result in a vertical line at the initial volume ().